https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Ifrim&feedformat=atomUW-Math Wiki - User contributions [en]2022-09-28T16:27:58ZUser contributionsMediaWiki 1.35.6https://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23743PDE Geometric Analysis seminar2022-09-21T19:28:41Z<p>Ifrim: </p>
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<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
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Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
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https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
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<br />
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[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
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<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
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<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
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=Fall 2022= <br />
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<br />
<br />
'''September 12, 2022'''<br />
<br />
[[No Seminar]]<br />
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'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran. <br />
<br />
Format: in-person. Time: 4-5PM, VV B139. <br />
<br />
Title: Homogenization in front propagation models<br />
<br />
Abstract: Homogenization is a general principle that the dynamics of physical processes occurring in periodic or random environments often become effectively homogeneous in the long-time-large-scale limit. I will presents results showing that homogenization occurs for reaction-diffusion equations with both time-periodic-spatially-random and space-time-random KPP reactions and coefficients. These results rely on two crucial new tools: virtual linearity of KPP reaction-diffusion dynamics and a non-autonomous versions of Kingman’s subadditive ergodic theorem.<br />
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'''September 26, 2022 ''' <br />
<br />
[[Haotian Wu]] (The University of Sydney, Australia). Host: Sigurd Angenent.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
<u>Title:</u> ''Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up''<br />
<br />
<u>Abstract:</u> The mean curvature flow (MCF) deforms a hypersurface in the direction of its mean curvature vectors. Singularities in mean curvature flow can form in either finite or infinite time. We present some results concerning the precise asymptotics of non-compact MCF solutions with either Type-IIa (in finite time) or Type-IIb (in infinite time) curvature blow-up. This is based on joint works with Jim Isenberg (Oregon) and Zhou Zhang (Sydney).<br />
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'''October 3, 2022'''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 10, 2022'''<br />
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[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 17, 2022'''<br />
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[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 24, 2022'''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 31, 2022 ''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 7, 2022 '''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 14, 2022 '''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 21, 2022 '''<br />
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[[Jason Murphy]] (Missouri S&T)<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 28, 2022 '''<br />
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[[No Seminar]]- Thanksgiving <br />
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<br />
<br />
<br />
<br />
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'''December 5, 2022 '''<br />
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[[James Rowan]] (UC Berkeley)<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''December 12, 2022 '''<br />
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[[Calumn Rickard ]] UC Davis<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
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<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
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<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
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<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
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<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
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<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23673PDE Geometric Analysis seminar2022-09-17T03:43:56Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
'''September 12, 2022'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran. <br />
<br />
Format: in-person. Time: 4-5PM, VV B139. <br />
<br />
Title: Homogenization in front propagation models<br />
<br />
Abstract: Homogenization is a general principle that the dynamics of physical processes occurring in periodic or random environments often become effectively homogeneous in the long-time-large-scale limit. I will presents results showing that homogenization occurs for reaction-diffusion equations with both time-periodic-spatially-random and space-time-random KPP reactions and coefficients. These results rely on two crucial new tools: virtual linearity of KPP reaction-diffusion dynamics and a non-autonomous versions of Kingman’s subadditive ergodic theorem.<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[Haotian Wu]] (The University of Sydney, Australia). Host: Sigurd Angenent.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
<u>Title:</u> ''Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up''<br />
<br />
<u>Abstract:</u> The mean curvature flow (MCF) deforms a hypersurface in the direction of its mean curvature vectors. Singularities in mean curvature flow can form in either finite or infinite time. We present some results concerning the precise asymptotics of non-compact MCF solutions with either Type-IIa (in finite time) or Type-IIb (in infinite time) curvature blow-up. This is based on joint works with Jim Isenberg (Oregon) and Zhou Zhang (Sydney).<br />
<br />
<br />
<br />
<br />
'''October 3, 2022'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022 ''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022 '''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022 '''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23672PDE Geometric Analysis seminar2022-09-17T03:43:23Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
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<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
'''September 12, 2022'''<br />
<br />
[[No Seminar]]<br />
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'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran. <br />
<br />
Format: in-person. Time: 4-5PM, VV B139. <br />
<br />
Title: Homogenization in front propagation models<br />
<br />
Abstract: Homogenization is a general principle that the dynamics of physical processes occurring in periodic or random environments often become effectively homogeneous in the long-time-large-scale limit. I will presents results showing that homogenization occurs for reaction-diffusion equations with both time-periodic-spatially-random and space-time-random KPP reactions and coefficients. These results rely on two crucial new tools: virtual linearity of KPP reaction-diffusion dynamics and a non-autonomous versions of Kingman’s subadditive ergodic theorem.<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
'''Haotian Wu''' (The University of Sydney, Australia). Host: Sigurd Angenent.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
<u>Title:</u> ''Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up''<br />
<br />
<u>Abstract:</u> The mean curvature flow (MCF) deforms a hypersurface in the direction of its mean curvature vectors. Singularities in mean curvature flow can form in either finite or infinite time. We present some results concerning the precise asymptotics of non-compact MCF solutions with either Type-IIa (in finite time) or Type-IIb (in infinite time) curvature blow-up. This is based on joint works with Jim Isenberg (Oregon) and Zhou Zhang (Sydney).<br />
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<br />
'''October 3, 2022'''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 10, 2022'''<br />
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[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 17, 2022'''<br />
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[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 24, 2022'''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''October 31, 2022 ''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 7, 2022 '''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 14, 2022 '''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''November 28, 2022 '''<br />
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[[No Seminar]]- Thanksgiving <br />
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<br />
<br />
<br />
<br />
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'''December 5, 2022 '''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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'''December 12, 2022 '''<br />
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[[TBA]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23671PDE Geometric Analysis seminar2022-09-17T03:42:51Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
'''September 12, 2022'''<br />
<br />
[[No Seminar]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran. <br />
<br />
Format: in-person. Time: 4-5PM, VV B139. <br />
<br />
Title: Homogenization in front propagation models<br />
<br />
Abstract: Homogenization is a general principle that the dynamics of physical processes occurring in periodic or random environments often become effectively homogeneous in the long-time-large-scale limit. I will presents results showing that homogenization occurs for reaction-diffusion equations with both time-periodic-spatially-random and space-time-random KPP reactions and coefficients. These results rely on two crucial new tools: virtual linearity of KPP reaction-diffusion dynamics and a non-autonomous versions of Kingman’s subadditive ergodic theorem.<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
'''Haotian Wu''' (The University of Sydney, Australia). Host: Sigurd Angenent.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
<u>Title:</u> ''Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up''<br />
<br />
<u>Abstract:</u> The mean curvature flow (MCF) deforms a hypersurface in the direction of its mean curvature vectors. Singularities in mean curvature flow can form in either finite or infinite time. We present some results concerning the precise asymptotics of non-compact MCF solutions with either Type-IIa (in finite time) or Type-IIb (in infinite time) curvature blow-up. This is based on joint works with Jim Isenberg (Oregon) and Zhou Zhang (Sydney).<br />
<br />
<br />
<br />
<br />
'''October 3, 2022'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022 ''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022 '''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022 '''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23540PDE Geometric Analysis seminar2022-09-01T17:47:35Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
'''September 12, 2022'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022 ''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022 '''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022 '''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022 '''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
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<br />
<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23539PDE Geometric Analysis seminar2022-09-01T17:46:31Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
'''September 12, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022.'''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022.'''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23538PDE Geometric Analysis seminar2022-09-01T17:44:03Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022.'''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022.'''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23537PDE Geometric Analysis seminar2022-09-01T17:43:24Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]]<br />
<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022.'''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022.'''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23536PDE Geometric Analysis seminar2022-09-01T17:42:15Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
<br />
<br />
[Please make sure to check the seminar webpage regularly so you will be constantly correctly informed on the format and time of the seminar.]<br />
<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022.'''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022.'''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23535PDE Geometric Analysis seminar2022-09-01T17:38:19Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022.'''<br />
<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]](Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 28, 2022.'''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022.'''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''December 12, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23534PDE Geometric Analysis seminar2022-09-01T17:35:35Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
[[Andrej Zlatos]] (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''September 26, 2022 ''' <br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022.'''<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
[[Yuan Gao]](Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 29, 2022.'''<br />
<br />
[[TBA]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''December 5, 2022.'''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23533PDE Geometric Analysis seminar2022-09-01T17:33:15Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
Andrej Zlatos (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
'''September 26, 2022 ''' <br />
<br />
TBA<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 3, 2022.'''<br />
TBA<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
Alexander Kiselev (Duke). Host: Sergey Denisov.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
Nicolas Garca Trillos (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''October 24, 2022.'''<br />
<br />
TBA<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
Yuan Gao (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 7, 2022.'''<br />
<br />
TBA<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 14, 2022.'''<br />
<br />
TBA<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
Jason Murphy (Missouri S&T)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
'''November 29, 2022.'''<br />
<br />
<br />
<br />
<br />
'''December 5, 2022.'''<br />
<br />
James Rowan (UC Berkeley)<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23532PDE Geometric Analysis seminar2022-09-01T17:28:51Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2022-Spring 2023 | Schedule for Fall 2022-Spring 2023]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Fall 2022= <br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
Andrej Zlatos (UCSD). Host: Hung Tran.<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
'''September 26, 2022 ''' <br />
<br />
TBA<br />
<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
'''October 3, 2022.'''<br />
TBA<br />
<br />
Format: , Time: 3:30-4:30PM <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
Alexander Kiselev (Duke). Host: Sergey Denisov.<br />
<br />
<br />
'''October 17, 2022.'''<br />
<br />
Nicolas Garca Trillos (Stats, UW Madison). Host: Hung Tran.<br />
<br />
<br />
'''October 31, 2022.''' (Tentative date, which might be changed)<br />
<br />
Yuan Gao (Purdue). Host: Hung Tran.<br />
<br />
<br />
'''November 21, 2022.'''<br />
<br />
Jason Murphy (Missouri S&T)<br />
<br />
'''December''' '''5, 2022.'''<br />
<br />
James Rowan (UC Berkeley)<br />
<br />
<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23332PDE Geometric Analysis seminar2022-07-13T09:43:58Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
Andrej Zlatos (UCSD). Host: Hung Tran.<br />
<br />
<br />
'''October 3, 2022''' (tentative date which can be changed).<br />
<br />
Nicolas Garca Trillos (Stats, UW Madison). Host: Hung Tran.<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
Alexander Kiselev (Duke). Host: Sergey Denisov.<br />
<br />
↵'''November 21, 2022.'''<br />
<br />
Jason Murphy (Missouri S&T)<br />
<br />
'''December''' '''5, 2022.'''<br />
<br />
James Rowan (UC Berkeley)<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23328PDE Geometric Analysis seminar2022-07-12T07:18:37Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
Andrej Zlatos (UCSD). Host: Hung Tran.<br />
<br />
<br />
'''October 3, 2022''' (tentative date which can be changed).<br />
<br />
Nicolas Garca Trillos (Stats, UW Madison). Host: Hung Tran.<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
Alexander Kiselev (Duke). Host: Sergey Denisov.<br />
<br />
'''December''' '''5, 2022.'''<br />
<br />
James Rowan (UC Berkeley)<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23327PDE Geometric Analysis seminar2022-07-12T07:16:39Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 [[Tel:5468 1353|5468 1353]]<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
Andrej Zlatos (UCSD). Host: Hung Tran.<br />
<br />
<br />
'''October 3, 2022''' (tentative date which can be changed).<br />
<br />
Nicolas Garca Trillos (Stats, UW Madison). Host: Hung Tran.<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
Alexander Kiselev (Duke). Host: Sergey Denisov.<br />
<br />
December '''5, 2022.'''<br />
<br />
James Rowan (UC Berkeley)<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23326PDE Geometric Analysis seminar2022-07-12T07:13:57Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
'''September 20, 2022 (Tuesday)''' joint PDE and Analysis Seminar<br />
<br />
Andrej Zlatos (UCSD). Host: Hung Tran.<br />
<br />
<br />
'''October 3, 2022''' (tentative date which can be changed).<br />
<br />
Nicolas Garca Trillos (Stats, UW Madison). Host: Hung Tran.<br />
<br />
<br />
'''October 10, 2022.'''<br />
<br />
Alexander Kiselev (Duke). Host: Sergey Denisov.<br />
<br />
‘’’December 5, 2022.’’’<br />
<br />
James Rowan (UC Berkeley)<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23106PDE Geometric Analysis seminar2022-04-11T17:41:30Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: The Carleman-based convexification approach for the 3D inverse scattering problem with experimental data.<br />
<br />
Abstract: We study the inverse scattering problem for the three-dimensional Helmholtz equation with multi-frequency back scattering data. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasi-linear elliptic partial differential equations. We solve this coupled system by developing the Carleman convexification method. Using the Carleman weight function, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. The Lipschitz stability estimate of the Carleman convexification method is proved also via a Carleman estimate. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data and experimental data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes, and dielectric constants.<br />
<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=23081Putnam Club2022-04-06T16:46:46Z<p>Ifrim: </p>
<hr />
<div>==Spring 2022==<br />
<br />
[[File:Bascom-fall-1500x500-1500x500.jpg ]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2022 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatyana Shcherbina, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from February 2) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://hilbert.math.wisc.edu/wiki/index.php/Undergraduate_Math_Competition The sixth UW Madison undergraduate math competition] will take place on Saturday, April 23! The exact time and location will be announced soon. </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting February 2, 2022<br />
Dima Arinkin<br />
|Meeting at the 9th floor lounge Van Vleck. When: February 2, 2022 05:00 PM. <br />
<br />
[[Media:Putnam101415.pdf | Matrices and determinants]]<br />
<br />
|-<br />
|Meeting February 9, 2022<br />
Dima Arinkin<br />
| [[Media:Putnam020922.pdf | Functions and calculus]]<br />
<br />
|-<br />
|Meeting February 16, 2022<br />
Tatyana Shcherbina<br />
|We are going to discuss [[Media:PutClub_S22_an.pdf | Analysis problems]]<br />
<br />
|-<br />
|Meeting February 23, 2022<br />
Tatyana Shcherbina<br />
|We are going to continue to discuss [[Media:PutClub_S22_an2.pdf | Analysis problems 2]]<br />
<br />
|-<br />
|Meeting March 2, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_graph_theory_2022_Botong.pdf | Graph theory]]<br />
<br />
|-<br />
|Meeting March 9, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_geometry_2022.pdf | Geometry]]<br />
<br />
|-<br />
|Meeting March 23, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam032322.pdf | Games]]<br />
<br />
|-<br />
|Meeting March 30, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam033022.pdf | Generating functions and telescoping series]]<br />
<br />
|-<br />
|Meeting April 6, 2022<br />
Mihaela Ifrim<br />
| [[Media: Competitions-m.pdf | Competition problems]]<br />
<br />
|-<br />
|Meeting April 13, 2022<br />
Mihaela Ifrim<br />
|<br />
<br />
|-<br />
|Meeting April 20, 2022<br />
Tatyana Shcherbina<br />
|<br />
<br />
|-<br />
|Meeting April 27, 2022<br />
Tatyana Shcherbina<br />
|<br />
|}<br />
</center><br />
<br />
[[File:WiscFall.jpg ]]<br />
<br />
==Fall 2021==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 22) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://www.maa.org/math-competitions/putnam-competition The 82nd Putnam competition] will take place on Saturday, December 4, at Van Vleck B123 (we will move the afternoon exam to B3 floor, most likely B333, due to noise issues) (9AM-Noon, 2PM-5PM). Make sure to register for the competition!!!</font></span><br />
<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting September 22, 2021<br />
Botong Wang<br />
|Meeting at the 9th floor lounge Van Vleck. When: Sep 22, 2021 05:00 PM. <br />
<br />
In the first two lectures, we will take a look at some of the Putnam competition problems from [https://kskedlaya.org/putnam-archive/2020.pdf 2020] and [https://kskedlaya.org/putnam-archive/2019.pdf 2019]. <br />
<br />
We plan to start with algebraic problems such as 2019 A1, A2, B1, B3, 2020 A1, A2, B1. Then continue to the analytic ones such as 2019 A3, A4, B2, 2020 A3. <br />
<br />
|-<br />
|Meeting September 29th, 2021<br />
Botong Wang <br />
<br />
<br />
|Continue the two sets of Putnam problems from last time. <br />
<br />
|-<br />
|Meeting October 6th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Polynomials. We'll look at the [[Media:Putnam100621-Polynomials.pdf | following problems]] (the last few problems are quite hard, and we probably won't get to them during the meeting).<br />
<br />
|-<br />
|Meeting October 13th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Continuing with the problems from last time. If you have the time, please look at the problems in advance, and then if you have ideas or questions, we would talk about it at the start. <br />
<br />
|-<br />
|Meeting October 20th, 2021<br />
Tatyana<br />
<br />
| We are going to discuss number theory problems. The plan is to look on some of the [[Media:PutClub_F21_nt.pdf | following problems]] (we probably will not cover them all)<br />
<br />
<br />
|-<br />
|Meeting October 27th, 2021<br />
Tatyana<br />
<br />
|We will continue to discuss some number theory problems from the list<br />
<br />
|-<br />
|Meeting November 3rd, 2021<br />
Botong<br />
<br />
|We are going to discuss [[Media:Putnam_inequalities_2021.pdf | Inequalities!]] <br />
<br />
|-<br />
|Meeting November 10th, 2021<br />
Botong<br />
<br />
|We continue the discussion of inequalities<br />
<br />
|-<br />
|Meeting November 17th, 2021<br />
Mihaela Ifrim<br />
<br />
|We started discussing [[Media:Putnam 11.24.2021.pdf | Various problems from past competitions]] <br />
<br />
<br />
|-<br />
|Meeting November 24th, 2021<br />
<br />
<br />
|Thanksgiving break<br />
<br />
|<br />
<br />
|-<br />
|Meeting December 1st, 2021<br />
Mihaela Ifrim<br />
<br />
|Working in the extra problems added to the Nov 17th pdf. Solutions to all the problems: [[Media:Putnam_11.22.2021_Sols.pdf | Various problems from past competitions]] <br />
<br />
|-<br />
|Meeting December 8th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the actual Putnam problems. Covered half of them.<br />
<br />
<br />
<br />
|-<br />
|Meeting December 15th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the remaining problems; we still have some left: A6 and B5. See you all after the Winter break!<br />
<br />
<br />
<br />
|}<br />
</center><br />
<br />
<br />
<br />
<br />
==Spring 2021==<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
Due to the coronavirus crisis, '''the 81st Putnam Competition''', originally scheduled for Fall 2020, has been postponed until Feb. 20, 2021. The competition was in an '''unofficial mode''', with no proctors, no prizes, no awards, and no national recognition of high-scoring individuals or teams. The solution papers are uploaded by participants for grading. Scores will be reported back privately to the individual participants and the local supervisor of each institution will receive a report of the scores of the students for that institution. <br />
<br />
'''We will not continue our Putnam club meetings after March 24. See you all in the fall!<br />
'''<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting Feb 10, 2021<br />
Botong Wang<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Feb 10, 2021 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJMrd-yhpjstHt34UK8YJ9_mZJ7NT_G3NLcM After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
The first two meetings will be presented by Botong. We will look at some of the most recent Putnam exams to help you prepare for the coming one. <br />
<br />
On Feb 10, we will go over some of the [https://www.maa.org/sites/default/files/pdf/Putnam/2019/2019PutnamProblems.pdf 2019 Putnam problems]. <br />
<br />
|-<br />
|Meeting Feb 17, 2021<br />
Botong Wang <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will continue to discuss problems in the 2019 Putnam competition. We will also look at some of the [https://kskedlaya.org/putnam-archive/2018.pdf 2018 Putnam problems]. </span> <br />
<br />
<br />
|-<br />
|Meeting Feb 24, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will look at some of the problems from [https://kskedlaya.org/putnam-archive/2020.pdf this year's Putnam] (which took place last weekend). </span> <br />
<br />
|-<br />
|Meeting Mar 3, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">Let's keep looking at the [https://kskedlaya.org/putnam-archive/2020.pdf Putnam problems] - some interesting ones left!</span> <br />
<br />
|-<br />
|Meeting Mar 10 and Mar 17, 2021<br />
Botong Wang<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will discuss several apects of combinatorics: graphs, set theory and geometric combinatorics. The worksheet is [[Media: Putnam_Combinatorics_2021.pdf | here]].</span> <br />
|<br />
<br />
|-<br />
|Meeting Mar 24, 2021<br />
Mihaela Ifrim<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will go over problems in linear algebra and analysis. The worksheet is [[Media: Putnam-Problems_and_Theory_form_March_23_2021.pdf | here]].</span><br />
|}<br />
<br />
<br />
<br />
==Fall 2020==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE FALL 2020 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson">However, this year things are a bit unusual. The 2020 Putnam competition is postponed until February 20, 2021. It is not determined yet whether the competition will be in person or online yet.Here is the original statement on the official webpage of the contest:</span> </div><br />
<br />
''Due to the coronavirus crisis, most students in the US and Canada are unable to return to campuses this fall. Therefore, the 81st Putnam Competition, originally scheduled for Fall 2020, will be postponed until February 20, 2021. If most students can return to campuses in the spring, the competition on that date can go forward in much the same form as in previous years. On the other hand, if most students are unable to return to campuses in the spring, the competition on that date will proceed in an unofficial mode, with no proctors, no prizes, no awards, but with solution papers submitted for grading by participants themselves and scores reported back privately to the individual participants.<br />
<br />
''<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;">[http://kskedlaya.org/putnam-archive/ <font size="3">Old exams and more information on the Putnam competition.</font>]</div></div><br />
<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ <span style="color:crimson"> over here.</div>] <br />
<br />
<div style="text-align: center;"><font size="3">'''We will have online meetings every Wednesday 5:00-6:30PM. ''' </font></div><br />
<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;"> <font size="3">The first meeting of this semester will happen on the 16th of September 2020! Please let all your colleagues know that we are continuing the Putnam Club and we are enthusiastic and hopeful we will keep you all engaged throughout the semester!</font> </div></div><br />
<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting 16 SEPT 2020<br />
Mihaela Ifrim<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Sep 16, 2020 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting:<br />
https://uwmadison.zoom.us/meeting/register/tJApcumhrz4pEtJRe_o0WTGM26u2zTM8T6J5 After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
You will meet us all at some point in time:) First two meetings will be presented by Mihaela. We will each teach two consecutive meetings. <br />
<br />
<span style="color:blue">UPDATE (09/17/2020): e met and all the documents (problems discussed and solutions given by you in class, are now shared with you via onedrive (app related to your outlook wisc account!)). I have also sent to you an invitation to use the witheboard attached to the same wisc account! But, do not feel discouraged in case you want to join later! You are always welcomed! </span><br />
<br />
<span style="color:green"> Please check out the following book: '''Putnam and Beyond'''! We will use it throughout the meetings!</span><br />
<br />
The first list of problems is posted! Please email me if you want access to it! [[File:Putnam_Problem_Set_1.pdf ]]<br />
<br />
<br />
|-<br />
|Meeting 23 SEPT 2020<br />
Mihaela Ifrim <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We discussed the problems given in the Putnam_Problem_Set_1 and their solutions are now posted on the shared folder.<br />
In addition I have also gave you the following problems to think at. [[File:Putnam_September_23_2020.pdf]]</span> <br />
<br />
<br />
<br />
<br />
|-<br />
|Meeting 30 SEPT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please consider joining ! <br />
<span style="color:Indigo">The next meeting will cover NUMBER THEORY! Please see the attached list of problems!! Enjoy!!! [[File:Putnam_nt1(1).pdf ]]</span><br />
<br />
<br />
<br />
|-<br />
|Meeting 7 OCT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam_nt2.pdf]] If you have solutions for the previous proposed set of problems, please email them so that we can compile a set of solutions. We will post them in our onedrive folder. If you are new, please email us and we will give access to it!<br />
|-<br />
<br />
-<br />
|Meeting 14 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] A more detailed list is posted on onedrive! <br />
|-<br />
<br />
-<br />
|Meeting 21 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! We worked out some of the problem proposed on the previous meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] Some solutions will be posted on onedrive! Reach out to us if you would like access to the solutions and you did not register yet! <br />
|-<br />
-<br />
|Meeting 28 OCT 2020<br />
Tatyana Shcherbina <br />
<br />
| ZOOM: Please join! The next two meeting will cover '''Polynomials'''! Please see the attached list of problems!! Enjoy!!! [[File: putnam_pol1.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the theory discussed on Oct 28 and hints to the problems [[File: putnam_pol1_hints.pdf ]] and [[File: polynomials_theory.pdf ]] <br />
|-<br />
<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the solutions of Polynomials problems [[File: putnam_Oct28_sol.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 11 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''Linear algebra'''. Here are the [[Media:linear_algebra_2020.pdf | problems]] I plan to discuss, and here is a short [http://math.northwestern.edu/putnam/filom/Linear_and_Abstract_Algebra.pdf summary] (from NWU) of some common linear algebra techniques for math contests.<br />
|-<br />
<br />
|Meeting 18 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). Continuing with the linear algebra: here are the [[Media:linear_algebra_2_2020.pdf | problems]] (including some left-overs from the last time). <br />
|-<br />
<br />
|Meeting 2 Dec 2020<br />
Botong Wang <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''limits of sequences''' (sections 3.1.3, 3.1.4, 3.1.5 in Putnam and Beyond). We will go over some basic theorems and discuss how to apply them. Here is the [[Media:Putnam_limits.pdf | worksheet]].<br />
|-<br />
|}<br />
<br />
<br />
----<br />
<br />
==Spring 2020==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. <br />
<br />
The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 5: [[Media:Putnam_Binomial2020.pdf | Binomial coefficients and generating functions]] [[Media:Putnam_Binomial2020_answer.pdf | (Answers and hints)]] Botong <br />
* February 19: [[Media:Putnam_Number_theory2020.pdf | Number theory]] [[Media:Putnam_Number2020.pdf | (Answers and hints)]] Botong<br />
* March 4 and 11: [[Media: Inequalities.pdf | Inequalities]] ( Note comming up!) Kim<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
* November 13: ??<br />
* November 20: [[Geometry.pdf | Geometry]] ( Note comming up!) Mihaela<br />
* November 27: [[No meeting! Thanksgiving! ]]<br />
* December 4: Last meeting of the semester! Please come and bring your friends too!! It will be fun! Mihaela<br />
<br />
<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other Olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=File:Competitions-m.pdf&diff=23080File:Competitions-m.pdf2022-04-06T16:46:30Z<p>Ifrim: </p>
<hr />
<div></div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=23079Putnam Club2022-04-06T16:45:43Z<p>Ifrim: </p>
<hr />
<div>==Spring 2022==<br />
<br />
[[File:Bascom-fall-1500x500-1500x500.jpg ]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2022 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatyana Shcherbina, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from February 2) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://hilbert.math.wisc.edu/wiki/index.php/Undergraduate_Math_Competition The sixth UW Madison undergraduate math competition] will take place on Saturday, April 23! The exact time and location will be announced soon. </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting February 2, 2022<br />
Dima Arinkin<br />
|Meeting at the 9th floor lounge Van Vleck. When: February 2, 2022 05:00 PM. <br />
<br />
[[Media:Putnam101415.pdf | Matrices and determinants]]<br />
<br />
|-<br />
|Meeting February 9, 2022<br />
Dima Arinkin<br />
| [[Media:Putnam020922.pdf | Functions and calculus]]<br />
<br />
|-<br />
|Meeting February 16, 2022<br />
Tatyana Shcherbina<br />
|We are going to discuss [[Media:PutClub_S22_an.pdf | Analysis problems]]<br />
<br />
|-<br />
|Meeting February 23, 2022<br />
Tatyana Shcherbina<br />
|We are going to continue to discuss [[Media:PutClub_S22_an2.pdf | Analysis problems 2]]<br />
<br />
|-<br />
|Meeting March 2, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_graph_theory_2022_Botong.pdf | Graph theory]]<br />
<br />
|-<br />
|Meeting March 9, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_geometry_2022.pdf | Geometry]]<br />
<br />
|-<br />
|Meeting March 23, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam032322.pdf | Games]]<br />
<br />
|-<br />
|Meeting March 30, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam033022.pdf | Generating functions and telescoping series]]<br />
<br />
|-<br />
|Meeting April 6, 2022<br />
Mihaela Ifrim<br />
| [[Media: Competitions.pdf | Competition problems]]<br />
<br />
|-<br />
|Meeting April 13, 2022<br />
Mihaela Ifrim<br />
|<br />
<br />
|-<br />
|Meeting April 20, 2022<br />
Tatyana Shcherbina<br />
|<br />
<br />
|-<br />
|Meeting April 27, 2022<br />
Tatyana Shcherbina<br />
|<br />
|}<br />
</center><br />
<br />
[[File:WiscFall.jpg ]]<br />
<br />
==Fall 2021==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 22) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://www.maa.org/math-competitions/putnam-competition The 82nd Putnam competition] will take place on Saturday, December 4, at Van Vleck B123 (we will move the afternoon exam to B3 floor, most likely B333, due to noise issues) (9AM-Noon, 2PM-5PM). Make sure to register for the competition!!!</font></span><br />
<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting September 22, 2021<br />
Botong Wang<br />
|Meeting at the 9th floor lounge Van Vleck. When: Sep 22, 2021 05:00 PM. <br />
<br />
In the first two lectures, we will take a look at some of the Putnam competition problems from [https://kskedlaya.org/putnam-archive/2020.pdf 2020] and [https://kskedlaya.org/putnam-archive/2019.pdf 2019]. <br />
<br />
We plan to start with algebraic problems such as 2019 A1, A2, B1, B3, 2020 A1, A2, B1. Then continue to the analytic ones such as 2019 A3, A4, B2, 2020 A3. <br />
<br />
|-<br />
|Meeting September 29th, 2021<br />
Botong Wang <br />
<br />
<br />
|Continue the two sets of Putnam problems from last time. <br />
<br />
|-<br />
|Meeting October 6th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Polynomials. We'll look at the [[Media:Putnam100621-Polynomials.pdf | following problems]] (the last few problems are quite hard, and we probably won't get to them during the meeting).<br />
<br />
|-<br />
|Meeting October 13th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Continuing with the problems from last time. If you have the time, please look at the problems in advance, and then if you have ideas or questions, we would talk about it at the start. <br />
<br />
|-<br />
|Meeting October 20th, 2021<br />
Tatyana<br />
<br />
| We are going to discuss number theory problems. The plan is to look on some of the [[Media:PutClub_F21_nt.pdf | following problems]] (we probably will not cover them all)<br />
<br />
<br />
|-<br />
|Meeting October 27th, 2021<br />
Tatyana<br />
<br />
|We will continue to discuss some number theory problems from the list<br />
<br />
|-<br />
|Meeting November 3rd, 2021<br />
Botong<br />
<br />
|We are going to discuss [[Media:Putnam_inequalities_2021.pdf | Inequalities!]] <br />
<br />
|-<br />
|Meeting November 10th, 2021<br />
Botong<br />
<br />
|We continue the discussion of inequalities<br />
<br />
|-<br />
|Meeting November 17th, 2021<br />
Mihaela Ifrim<br />
<br />
|We started discussing [[Media:Putnam 11.24.2021.pdf | Various problems from past competitions]] <br />
<br />
<br />
|-<br />
|Meeting November 24th, 2021<br />
<br />
<br />
|Thanksgiving break<br />
<br />
|<br />
<br />
|-<br />
|Meeting December 1st, 2021<br />
Mihaela Ifrim<br />
<br />
|Working in the extra problems added to the Nov 17th pdf. Solutions to all the problems: [[Media:Putnam_11.22.2021_Sols.pdf | Various problems from past competitions]] <br />
<br />
|-<br />
|Meeting December 8th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the actual Putnam problems. Covered half of them.<br />
<br />
<br />
<br />
|-<br />
|Meeting December 15th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the remaining problems; we still have some left: A6 and B5. See you all after the Winter break!<br />
<br />
<br />
<br />
|}<br />
</center><br />
<br />
<br />
<br />
<br />
==Spring 2021==<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
Due to the coronavirus crisis, '''the 81st Putnam Competition''', originally scheduled for Fall 2020, has been postponed until Feb. 20, 2021. The competition was in an '''unofficial mode''', with no proctors, no prizes, no awards, and no national recognition of high-scoring individuals or teams. The solution papers are uploaded by participants for grading. Scores will be reported back privately to the individual participants and the local supervisor of each institution will receive a report of the scores of the students for that institution. <br />
<br />
'''We will not continue our Putnam club meetings after March 24. See you all in the fall!<br />
'''<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting Feb 10, 2021<br />
Botong Wang<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Feb 10, 2021 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJMrd-yhpjstHt34UK8YJ9_mZJ7NT_G3NLcM After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
The first two meetings will be presented by Botong. We will look at some of the most recent Putnam exams to help you prepare for the coming one. <br />
<br />
On Feb 10, we will go over some of the [https://www.maa.org/sites/default/files/pdf/Putnam/2019/2019PutnamProblems.pdf 2019 Putnam problems]. <br />
<br />
|-<br />
|Meeting Feb 17, 2021<br />
Botong Wang <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will continue to discuss problems in the 2019 Putnam competition. We will also look at some of the [https://kskedlaya.org/putnam-archive/2018.pdf 2018 Putnam problems]. </span> <br />
<br />
<br />
|-<br />
|Meeting Feb 24, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will look at some of the problems from [https://kskedlaya.org/putnam-archive/2020.pdf this year's Putnam] (which took place last weekend). </span> <br />
<br />
|-<br />
|Meeting Mar 3, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">Let's keep looking at the [https://kskedlaya.org/putnam-archive/2020.pdf Putnam problems] - some interesting ones left!</span> <br />
<br />
|-<br />
|Meeting Mar 10 and Mar 17, 2021<br />
Botong Wang<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will discuss several apects of combinatorics: graphs, set theory and geometric combinatorics. The worksheet is [[Media: Putnam_Combinatorics_2021.pdf | here]].</span> <br />
|<br />
<br />
|-<br />
|Meeting Mar 24, 2021<br />
Mihaela Ifrim<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will go over problems in linear algebra and analysis. The worksheet is [[Media: Putnam-Problems_and_Theory_form_March_23_2021.pdf | here]].</span><br />
|}<br />
<br />
<br />
<br />
==Fall 2020==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE FALL 2020 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson">However, this year things are a bit unusual. The 2020 Putnam competition is postponed until February 20, 2021. It is not determined yet whether the competition will be in person or online yet.Here is the original statement on the official webpage of the contest:</span> </div><br />
<br />
''Due to the coronavirus crisis, most students in the US and Canada are unable to return to campuses this fall. Therefore, the 81st Putnam Competition, originally scheduled for Fall 2020, will be postponed until February 20, 2021. If most students can return to campuses in the spring, the competition on that date can go forward in much the same form as in previous years. On the other hand, if most students are unable to return to campuses in the spring, the competition on that date will proceed in an unofficial mode, with no proctors, no prizes, no awards, but with solution papers submitted for grading by participants themselves and scores reported back privately to the individual participants.<br />
<br />
''<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;">[http://kskedlaya.org/putnam-archive/ <font size="3">Old exams and more information on the Putnam competition.</font>]</div></div><br />
<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ <span style="color:crimson"> over here.</div>] <br />
<br />
<div style="text-align: center;"><font size="3">'''We will have online meetings every Wednesday 5:00-6:30PM. ''' </font></div><br />
<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;"> <font size="3">The first meeting of this semester will happen on the 16th of September 2020! Please let all your colleagues know that we are continuing the Putnam Club and we are enthusiastic and hopeful we will keep you all engaged throughout the semester!</font> </div></div><br />
<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting 16 SEPT 2020<br />
Mihaela Ifrim<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Sep 16, 2020 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting:<br />
https://uwmadison.zoom.us/meeting/register/tJApcumhrz4pEtJRe_o0WTGM26u2zTM8T6J5 After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
You will meet us all at some point in time:) First two meetings will be presented by Mihaela. We will each teach two consecutive meetings. <br />
<br />
<span style="color:blue">UPDATE (09/17/2020): e met and all the documents (problems discussed and solutions given by you in class, are now shared with you via onedrive (app related to your outlook wisc account!)). I have also sent to you an invitation to use the witheboard attached to the same wisc account! But, do not feel discouraged in case you want to join later! You are always welcomed! </span><br />
<br />
<span style="color:green"> Please check out the following book: '''Putnam and Beyond'''! We will use it throughout the meetings!</span><br />
<br />
The first list of problems is posted! Please email me if you want access to it! [[File:Putnam_Problem_Set_1.pdf ]]<br />
<br />
<br />
|-<br />
|Meeting 23 SEPT 2020<br />
Mihaela Ifrim <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We discussed the problems given in the Putnam_Problem_Set_1 and their solutions are now posted on the shared folder.<br />
In addition I have also gave you the following problems to think at. [[File:Putnam_September_23_2020.pdf]]</span> <br />
<br />
<br />
<br />
<br />
|-<br />
|Meeting 30 SEPT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please consider joining ! <br />
<span style="color:Indigo">The next meeting will cover NUMBER THEORY! Please see the attached list of problems!! Enjoy!!! [[File:Putnam_nt1(1).pdf ]]</span><br />
<br />
<br />
<br />
|-<br />
|Meeting 7 OCT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam_nt2.pdf]] If you have solutions for the previous proposed set of problems, please email them so that we can compile a set of solutions. We will post them in our onedrive folder. If you are new, please email us and we will give access to it!<br />
|-<br />
<br />
-<br />
|Meeting 14 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] A more detailed list is posted on onedrive! <br />
|-<br />
<br />
-<br />
|Meeting 21 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! We worked out some of the problem proposed on the previous meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] Some solutions will be posted on onedrive! Reach out to us if you would like access to the solutions and you did not register yet! <br />
|-<br />
-<br />
|Meeting 28 OCT 2020<br />
Tatyana Shcherbina <br />
<br />
| ZOOM: Please join! The next two meeting will cover '''Polynomials'''! Please see the attached list of problems!! Enjoy!!! [[File: putnam_pol1.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the theory discussed on Oct 28 and hints to the problems [[File: putnam_pol1_hints.pdf ]] and [[File: polynomials_theory.pdf ]] <br />
|-<br />
<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the solutions of Polynomials problems [[File: putnam_Oct28_sol.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 11 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''Linear algebra'''. Here are the [[Media:linear_algebra_2020.pdf | problems]] I plan to discuss, and here is a short [http://math.northwestern.edu/putnam/filom/Linear_and_Abstract_Algebra.pdf summary] (from NWU) of some common linear algebra techniques for math contests.<br />
|-<br />
<br />
|Meeting 18 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). Continuing with the linear algebra: here are the [[Media:linear_algebra_2_2020.pdf | problems]] (including some left-overs from the last time). <br />
|-<br />
<br />
|Meeting 2 Dec 2020<br />
Botong Wang <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''limits of sequences''' (sections 3.1.3, 3.1.4, 3.1.5 in Putnam and Beyond). We will go over some basic theorems and discuss how to apply them. Here is the [[Media:Putnam_limits.pdf | worksheet]].<br />
|-<br />
|}<br />
<br />
<br />
----<br />
<br />
==Spring 2020==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. <br />
<br />
The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 5: [[Media:Putnam_Binomial2020.pdf | Binomial coefficients and generating functions]] [[Media:Putnam_Binomial2020_answer.pdf | (Answers and hints)]] Botong <br />
* February 19: [[Media:Putnam_Number_theory2020.pdf | Number theory]] [[Media:Putnam_Number2020.pdf | (Answers and hints)]] Botong<br />
* March 4 and 11: [[Media: Inequalities.pdf | Inequalities]] ( Note comming up!) Kim<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
* November 13: ??<br />
* November 20: [[Geometry.pdf | Geometry]] ( Note comming up!) Mihaela<br />
* November 27: [[No meeting! Thanksgiving! ]]<br />
* December 4: Last meeting of the semester! Please come and bring your friends too!! It will be fun! Mihaela<br />
<br />
<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other Olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=23078Putnam Club2022-04-06T16:45:13Z<p>Ifrim: </p>
<hr />
<div>==Spring 2022==<br />
<br />
[[File:Bascom-fall-1500x500-1500x500.jpg ]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2022 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatyana Shcherbina, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from February 2) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://hilbert.math.wisc.edu/wiki/index.php/Undergraduate_Math_Competition The sixth UW Madison undergraduate math competition] will take place on Saturday, April 23! The exact time and location will be announced soon. </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting February 2, 2022<br />
Dima Arinkin<br />
|Meeting at the 9th floor lounge Van Vleck. When: February 2, 2022 05:00 PM. <br />
<br />
[[Media:Putnam101415.pdf | Matrices and determinants]]<br />
<br />
|-<br />
|Meeting February 9, 2022<br />
Dima Arinkin<br />
| [[Media:Putnam020922.pdf | Functions and calculus]]<br />
<br />
|-<br />
|Meeting February 16, 2022<br />
Tatyana Shcherbina<br />
|We are going to discuss [[Media:PutClub_S22_an.pdf | Analysis problems]]<br />
<br />
|-<br />
|Meeting February 23, 2022<br />
Tatyana Shcherbina<br />
|We are going to continue to discuss [[Media:PutClub_S22_an2.pdf | Analysis problems 2]]<br />
<br />
|-<br />
|Meeting March 2, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_graph_theory_2022_Botong.pdf | Graph theory]]<br />
<br />
|-<br />
|Meeting March 9, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_geometry_2022.pdf | Geometry]]<br />
<br />
|-<br />
|Meeting March 23, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam032322.pdf | Games]]<br />
<br />
|-<br />
|Meeting March 30, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam033022.pdf | Generating functions and telescoping series]]<br />
<br />
|-<br />
|Meeting April 6, 2022<br />
Mihaela Ifrim<br />
| [[Media: Competition.pdf | Competition problems]]<br />
<br />
|-<br />
|Meeting April 13, 2022<br />
Mihaela Ifrim<br />
|<br />
<br />
|-<br />
|Meeting April 20, 2022<br />
Tatyana Shcherbina<br />
|<br />
<br />
|-<br />
|Meeting April 27, 2022<br />
Tatyana Shcherbina<br />
|<br />
|}<br />
</center><br />
<br />
[[File:WiscFall.jpg ]]<br />
<br />
==Fall 2021==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 22) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://www.maa.org/math-competitions/putnam-competition The 82nd Putnam competition] will take place on Saturday, December 4, at Van Vleck B123 (we will move the afternoon exam to B3 floor, most likely B333, due to noise issues) (9AM-Noon, 2PM-5PM). Make sure to register for the competition!!!</font></span><br />
<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting September 22, 2021<br />
Botong Wang<br />
|Meeting at the 9th floor lounge Van Vleck. When: Sep 22, 2021 05:00 PM. <br />
<br />
In the first two lectures, we will take a look at some of the Putnam competition problems from [https://kskedlaya.org/putnam-archive/2020.pdf 2020] and [https://kskedlaya.org/putnam-archive/2019.pdf 2019]. <br />
<br />
We plan to start with algebraic problems such as 2019 A1, A2, B1, B3, 2020 A1, A2, B1. Then continue to the analytic ones such as 2019 A3, A4, B2, 2020 A3. <br />
<br />
|-<br />
|Meeting September 29th, 2021<br />
Botong Wang <br />
<br />
<br />
|Continue the two sets of Putnam problems from last time. <br />
<br />
|-<br />
|Meeting October 6th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Polynomials. We'll look at the [[Media:Putnam100621-Polynomials.pdf | following problems]] (the last few problems are quite hard, and we probably won't get to them during the meeting).<br />
<br />
|-<br />
|Meeting October 13th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Continuing with the problems from last time. If you have the time, please look at the problems in advance, and then if you have ideas or questions, we would talk about it at the start. <br />
<br />
|-<br />
|Meeting October 20th, 2021<br />
Tatyana<br />
<br />
| We are going to discuss number theory problems. The plan is to look on some of the [[Media:PutClub_F21_nt.pdf | following problems]] (we probably will not cover them all)<br />
<br />
<br />
|-<br />
|Meeting October 27th, 2021<br />
Tatyana<br />
<br />
|We will continue to discuss some number theory problems from the list<br />
<br />
|-<br />
|Meeting November 3rd, 2021<br />
Botong<br />
<br />
|We are going to discuss [[Media:Putnam_inequalities_2021.pdf | Inequalities!]] <br />
<br />
|-<br />
|Meeting November 10th, 2021<br />
Botong<br />
<br />
|We continue the discussion of inequalities<br />
<br />
|-<br />
|Meeting November 17th, 2021<br />
Mihaela Ifrim<br />
<br />
|We started discussing [[Media:Putnam 11.24.2021.pdf | Various problems from past competitions]] <br />
<br />
<br />
|-<br />
|Meeting November 24th, 2021<br />
<br />
<br />
|Thanksgiving break<br />
<br />
|<br />
<br />
|-<br />
|Meeting December 1st, 2021<br />
Mihaela Ifrim<br />
<br />
|Working in the extra problems added to the Nov 17th pdf. Solutions to all the problems: [[Media:Putnam_11.22.2021_Sols.pdf | Various problems from past competitions]] <br />
<br />
|-<br />
|Meeting December 8th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the actual Putnam problems. Covered half of them.<br />
<br />
<br />
<br />
|-<br />
|Meeting December 15th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the remaining problems; we still have some left: A6 and B5. See you all after the Winter break!<br />
<br />
<br />
<br />
|}<br />
</center><br />
<br />
<br />
<br />
<br />
==Spring 2021==<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
Due to the coronavirus crisis, '''the 81st Putnam Competition''', originally scheduled for Fall 2020, has been postponed until Feb. 20, 2021. The competition was in an '''unofficial mode''', with no proctors, no prizes, no awards, and no national recognition of high-scoring individuals or teams. The solution papers are uploaded by participants for grading. Scores will be reported back privately to the individual participants and the local supervisor of each institution will receive a report of the scores of the students for that institution. <br />
<br />
'''We will not continue our Putnam club meetings after March 24. See you all in the fall!<br />
'''<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting Feb 10, 2021<br />
Botong Wang<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Feb 10, 2021 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJMrd-yhpjstHt34UK8YJ9_mZJ7NT_G3NLcM After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
The first two meetings will be presented by Botong. We will look at some of the most recent Putnam exams to help you prepare for the coming one. <br />
<br />
On Feb 10, we will go over some of the [https://www.maa.org/sites/default/files/pdf/Putnam/2019/2019PutnamProblems.pdf 2019 Putnam problems]. <br />
<br />
|-<br />
|Meeting Feb 17, 2021<br />
Botong Wang <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will continue to discuss problems in the 2019 Putnam competition. We will also look at some of the [https://kskedlaya.org/putnam-archive/2018.pdf 2018 Putnam problems]. </span> <br />
<br />
<br />
|-<br />
|Meeting Feb 24, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will look at some of the problems from [https://kskedlaya.org/putnam-archive/2020.pdf this year's Putnam] (which took place last weekend). </span> <br />
<br />
|-<br />
|Meeting Mar 3, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">Let's keep looking at the [https://kskedlaya.org/putnam-archive/2020.pdf Putnam problems] - some interesting ones left!</span> <br />
<br />
|-<br />
|Meeting Mar 10 and Mar 17, 2021<br />
Botong Wang<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will discuss several apects of combinatorics: graphs, set theory and geometric combinatorics. The worksheet is [[Media: Putnam_Combinatorics_2021.pdf | here]].</span> <br />
|<br />
<br />
|-<br />
|Meeting Mar 24, 2021<br />
Mihaela Ifrim<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will go over problems in linear algebra and analysis. The worksheet is [[Media: Putnam-Problems_and_Theory_form_March_23_2021.pdf | here]].</span><br />
|}<br />
<br />
<br />
<br />
==Fall 2020==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE FALL 2020 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson">However, this year things are a bit unusual. The 2020 Putnam competition is postponed until February 20, 2021. It is not determined yet whether the competition will be in person or online yet.Here is the original statement on the official webpage of the contest:</span> </div><br />
<br />
''Due to the coronavirus crisis, most students in the US and Canada are unable to return to campuses this fall. Therefore, the 81st Putnam Competition, originally scheduled for Fall 2020, will be postponed until February 20, 2021. If most students can return to campuses in the spring, the competition on that date can go forward in much the same form as in previous years. On the other hand, if most students are unable to return to campuses in the spring, the competition on that date will proceed in an unofficial mode, with no proctors, no prizes, no awards, but with solution papers submitted for grading by participants themselves and scores reported back privately to the individual participants.<br />
<br />
''<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;">[http://kskedlaya.org/putnam-archive/ <font size="3">Old exams and more information on the Putnam competition.</font>]</div></div><br />
<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ <span style="color:crimson"> over here.</div>] <br />
<br />
<div style="text-align: center;"><font size="3">'''We will have online meetings every Wednesday 5:00-6:30PM. ''' </font></div><br />
<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;"> <font size="3">The first meeting of this semester will happen on the 16th of September 2020! Please let all your colleagues know that we are continuing the Putnam Club and we are enthusiastic and hopeful we will keep you all engaged throughout the semester!</font> </div></div><br />
<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting 16 SEPT 2020<br />
Mihaela Ifrim<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Sep 16, 2020 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting:<br />
https://uwmadison.zoom.us/meeting/register/tJApcumhrz4pEtJRe_o0WTGM26u2zTM8T6J5 After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
You will meet us all at some point in time:) First two meetings will be presented by Mihaela. We will each teach two consecutive meetings. <br />
<br />
<span style="color:blue">UPDATE (09/17/2020): e met and all the documents (problems discussed and solutions given by you in class, are now shared with you via onedrive (app related to your outlook wisc account!)). I have also sent to you an invitation to use the witheboard attached to the same wisc account! But, do not feel discouraged in case you want to join later! You are always welcomed! </span><br />
<br />
<span style="color:green"> Please check out the following book: '''Putnam and Beyond'''! We will use it throughout the meetings!</span><br />
<br />
The first list of problems is posted! Please email me if you want access to it! [[File:Putnam_Problem_Set_1.pdf ]]<br />
<br />
<br />
|-<br />
|Meeting 23 SEPT 2020<br />
Mihaela Ifrim <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We discussed the problems given in the Putnam_Problem_Set_1 and their solutions are now posted on the shared folder.<br />
In addition I have also gave you the following problems to think at. [[File:Putnam_September_23_2020.pdf]]</span> <br />
<br />
<br />
<br />
<br />
|-<br />
|Meeting 30 SEPT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please consider joining ! <br />
<span style="color:Indigo">The next meeting will cover NUMBER THEORY! Please see the attached list of problems!! Enjoy!!! [[File:Putnam_nt1(1).pdf ]]</span><br />
<br />
<br />
<br />
|-<br />
|Meeting 7 OCT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam_nt2.pdf]] If you have solutions for the previous proposed set of problems, please email them so that we can compile a set of solutions. We will post them in our onedrive folder. If you are new, please email us and we will give access to it!<br />
|-<br />
<br />
-<br />
|Meeting 14 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] A more detailed list is posted on onedrive! <br />
|-<br />
<br />
-<br />
|Meeting 21 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! We worked out some of the problem proposed on the previous meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] Some solutions will be posted on onedrive! Reach out to us if you would like access to the solutions and you did not register yet! <br />
|-<br />
-<br />
|Meeting 28 OCT 2020<br />
Tatyana Shcherbina <br />
<br />
| ZOOM: Please join! The next two meeting will cover '''Polynomials'''! Please see the attached list of problems!! Enjoy!!! [[File: putnam_pol1.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the theory discussed on Oct 28 and hints to the problems [[File: putnam_pol1_hints.pdf ]] and [[File: polynomials_theory.pdf ]] <br />
|-<br />
<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the solutions of Polynomials problems [[File: putnam_Oct28_sol.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 11 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''Linear algebra'''. Here are the [[Media:linear_algebra_2020.pdf | problems]] I plan to discuss, and here is a short [http://math.northwestern.edu/putnam/filom/Linear_and_Abstract_Algebra.pdf summary] (from NWU) of some common linear algebra techniques for math contests.<br />
|-<br />
<br />
|Meeting 18 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). Continuing with the linear algebra: here are the [[Media:linear_algebra_2_2020.pdf | problems]] (including some left-overs from the last time). <br />
|-<br />
<br />
|Meeting 2 Dec 2020<br />
Botong Wang <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''limits of sequences''' (sections 3.1.3, 3.1.4, 3.1.5 in Putnam and Beyond). We will go over some basic theorems and discuss how to apply them. Here is the [[Media:Putnam_limits.pdf | worksheet]].<br />
|-<br />
|}<br />
<br />
<br />
----<br />
<br />
==Spring 2020==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. <br />
<br />
The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 5: [[Media:Putnam_Binomial2020.pdf | Binomial coefficients and generating functions]] [[Media:Putnam_Binomial2020_answer.pdf | (Answers and hints)]] Botong <br />
* February 19: [[Media:Putnam_Number_theory2020.pdf | Number theory]] [[Media:Putnam_Number2020.pdf | (Answers and hints)]] Botong<br />
* March 4 and 11: [[Media: Inequalities.pdf | Inequalities]] ( Note comming up!) Kim<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
* November 13: ??<br />
* November 20: [[Geometry.pdf | Geometry]] ( Note comming up!) Mihaela<br />
* November 27: [[No meeting! Thanksgiving! ]]<br />
* December 4: Last meeting of the semester! Please come and bring your friends too!! It will be fun! Mihaela<br />
<br />
<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other Olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=File:Competition.pdf&diff=23077File:Competition.pdf2022-04-06T16:44:51Z<p>Ifrim: </p>
<hr />
<div></div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=23076Putnam Club2022-04-06T16:43:25Z<p>Ifrim: </p>
<hr />
<div>==Spring 2022==<br />
<br />
[[File:Bascom-fall-1500x500-1500x500.jpg ]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2022 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatyana Shcherbina, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from February 2) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://hilbert.math.wisc.edu/wiki/index.php/Undergraduate_Math_Competition The sixth UW Madison undergraduate math competition] will take place on Saturday, April 23! The exact time and location will be announced soon. </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting February 2, 2022<br />
Dima Arinkin<br />
|Meeting at the 9th floor lounge Van Vleck. When: February 2, 2022 05:00 PM. <br />
<br />
[[Media:Putnam101415.pdf | Matrices and determinants]]<br />
<br />
|-<br />
|Meeting February 9, 2022<br />
Dima Arinkin<br />
| [[Media:Putnam020922.pdf | Functions and calculus]]<br />
<br />
|-<br />
|Meeting February 16, 2022<br />
Tatyana Shcherbina<br />
|We are going to discuss [[Media:PutClub_S22_an.pdf | Analysis problems]]<br />
<br />
|-<br />
|Meeting February 23, 2022<br />
Tatyana Shcherbina<br />
|We are going to continue to discuss [[Media:PutClub_S22_an2.pdf | Analysis problems 2]]<br />
<br />
|-<br />
|Meeting March 2, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_graph_theory_2022_Botong.pdf | Graph theory]]<br />
<br />
|-<br />
|Meeting March 9, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_geometry_2022.pdf | Geometry]]<br />
<br />
|-<br />
|Meeting March 23, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam032322.pdf | Games]]<br />
<br />
|-<br />
|Meeting March 30, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam033022.pdf | Generating functions and telescoping series]]<br />
<br />
|-<br />
|Meeting April 6, 2022<br />
Mihaela Ifrim<br />
| [[Media: Competition_problems.pdf | Competition problems]]<br />
<br />
|-<br />
|Meeting April 13, 2022<br />
Mihaela Ifrim<br />
|<br />
<br />
|-<br />
|Meeting April 20, 2022<br />
Tatyana Shcherbina<br />
|<br />
<br />
|-<br />
|Meeting April 27, 2022<br />
Tatyana Shcherbina<br />
|<br />
|}<br />
</center><br />
<br />
[[File:WiscFall.jpg ]]<br />
<br />
==Fall 2021==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 22) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://www.maa.org/math-competitions/putnam-competition The 82nd Putnam competition] will take place on Saturday, December 4, at Van Vleck B123 (we will move the afternoon exam to B3 floor, most likely B333, due to noise issues) (9AM-Noon, 2PM-5PM). Make sure to register for the competition!!!</font></span><br />
<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting September 22, 2021<br />
Botong Wang<br />
|Meeting at the 9th floor lounge Van Vleck. When: Sep 22, 2021 05:00 PM. <br />
<br />
In the first two lectures, we will take a look at some of the Putnam competition problems from [https://kskedlaya.org/putnam-archive/2020.pdf 2020] and [https://kskedlaya.org/putnam-archive/2019.pdf 2019]. <br />
<br />
We plan to start with algebraic problems such as 2019 A1, A2, B1, B3, 2020 A1, A2, B1. Then continue to the analytic ones such as 2019 A3, A4, B2, 2020 A3. <br />
<br />
|-<br />
|Meeting September 29th, 2021<br />
Botong Wang <br />
<br />
<br />
|Continue the two sets of Putnam problems from last time. <br />
<br />
|-<br />
|Meeting October 6th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Polynomials. We'll look at the [[Media:Putnam100621-Polynomials.pdf | following problems]] (the last few problems are quite hard, and we probably won't get to them during the meeting).<br />
<br />
|-<br />
|Meeting October 13th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Continuing with the problems from last time. If you have the time, please look at the problems in advance, and then if you have ideas or questions, we would talk about it at the start. <br />
<br />
|-<br />
|Meeting October 20th, 2021<br />
Tatyana<br />
<br />
| We are going to discuss number theory problems. The plan is to look on some of the [[Media:PutClub_F21_nt.pdf | following problems]] (we probably will not cover them all)<br />
<br />
<br />
|-<br />
|Meeting October 27th, 2021<br />
Tatyana<br />
<br />
|We will continue to discuss some number theory problems from the list<br />
<br />
|-<br />
|Meeting November 3rd, 2021<br />
Botong<br />
<br />
|We are going to discuss [[Media:Putnam_inequalities_2021.pdf | Inequalities!]] <br />
<br />
|-<br />
|Meeting November 10th, 2021<br />
Botong<br />
<br />
|We continue the discussion of inequalities<br />
<br />
|-<br />
|Meeting November 17th, 2021<br />
Mihaela Ifrim<br />
<br />
|We started discussing [[Media:Putnam 11.24.2021.pdf | Various problems from past competitions]] <br />
<br />
<br />
|-<br />
|Meeting November 24th, 2021<br />
<br />
<br />
|Thanksgiving break<br />
<br />
|<br />
<br />
|-<br />
|Meeting December 1st, 2021<br />
Mihaela Ifrim<br />
<br />
|Working in the extra problems added to the Nov 17th pdf. Solutions to all the problems: [[Media:Putnam_11.22.2021_Sols.pdf | Various problems from past competitions]] <br />
<br />
|-<br />
|Meeting December 8th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the actual Putnam problems. Covered half of them.<br />
<br />
<br />
<br />
|-<br />
|Meeting December 15th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the remaining problems; we still have some left: A6 and B5. See you all after the Winter break!<br />
<br />
<br />
<br />
|}<br />
</center><br />
<br />
<br />
<br />
<br />
==Spring 2021==<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
Due to the coronavirus crisis, '''the 81st Putnam Competition''', originally scheduled for Fall 2020, has been postponed until Feb. 20, 2021. The competition was in an '''unofficial mode''', with no proctors, no prizes, no awards, and no national recognition of high-scoring individuals or teams. The solution papers are uploaded by participants for grading. Scores will be reported back privately to the individual participants and the local supervisor of each institution will receive a report of the scores of the students for that institution. <br />
<br />
'''We will not continue our Putnam club meetings after March 24. See you all in the fall!<br />
'''<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting Feb 10, 2021<br />
Botong Wang<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Feb 10, 2021 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJMrd-yhpjstHt34UK8YJ9_mZJ7NT_G3NLcM After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
The first two meetings will be presented by Botong. We will look at some of the most recent Putnam exams to help you prepare for the coming one. <br />
<br />
On Feb 10, we will go over some of the [https://www.maa.org/sites/default/files/pdf/Putnam/2019/2019PutnamProblems.pdf 2019 Putnam problems]. <br />
<br />
|-<br />
|Meeting Feb 17, 2021<br />
Botong Wang <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will continue to discuss problems in the 2019 Putnam competition. We will also look at some of the [https://kskedlaya.org/putnam-archive/2018.pdf 2018 Putnam problems]. </span> <br />
<br />
<br />
|-<br />
|Meeting Feb 24, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will look at some of the problems from [https://kskedlaya.org/putnam-archive/2020.pdf this year's Putnam] (which took place last weekend). </span> <br />
<br />
|-<br />
|Meeting Mar 3, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">Let's keep looking at the [https://kskedlaya.org/putnam-archive/2020.pdf Putnam problems] - some interesting ones left!</span> <br />
<br />
|-<br />
|Meeting Mar 10 and Mar 17, 2021<br />
Botong Wang<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will discuss several apects of combinatorics: graphs, set theory and geometric combinatorics. The worksheet is [[Media: Putnam_Combinatorics_2021.pdf | here]].</span> <br />
|<br />
<br />
|-<br />
|Meeting Mar 24, 2021<br />
Mihaela Ifrim<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will go over problems in linear algebra and analysis. The worksheet is [[Media: Putnam-Problems_and_Theory_form_March_23_2021.pdf | here]].</span><br />
|}<br />
<br />
<br />
<br />
==Fall 2020==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE FALL 2020 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson">However, this year things are a bit unusual. The 2020 Putnam competition is postponed until February 20, 2021. It is not determined yet whether the competition will be in person or online yet.Here is the original statement on the official webpage of the contest:</span> </div><br />
<br />
''Due to the coronavirus crisis, most students in the US and Canada are unable to return to campuses this fall. Therefore, the 81st Putnam Competition, originally scheduled for Fall 2020, will be postponed until February 20, 2021. If most students can return to campuses in the spring, the competition on that date can go forward in much the same form as in previous years. On the other hand, if most students are unable to return to campuses in the spring, the competition on that date will proceed in an unofficial mode, with no proctors, no prizes, no awards, but with solution papers submitted for grading by participants themselves and scores reported back privately to the individual participants.<br />
<br />
''<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;">[http://kskedlaya.org/putnam-archive/ <font size="3">Old exams and more information on the Putnam competition.</font>]</div></div><br />
<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ <span style="color:crimson"> over here.</div>] <br />
<br />
<div style="text-align: center;"><font size="3">'''We will have online meetings every Wednesday 5:00-6:30PM. ''' </font></div><br />
<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;"> <font size="3">The first meeting of this semester will happen on the 16th of September 2020! Please let all your colleagues know that we are continuing the Putnam Club and we are enthusiastic and hopeful we will keep you all engaged throughout the semester!</font> </div></div><br />
<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting 16 SEPT 2020<br />
Mihaela Ifrim<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Sep 16, 2020 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting:<br />
https://uwmadison.zoom.us/meeting/register/tJApcumhrz4pEtJRe_o0WTGM26u2zTM8T6J5 After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
You will meet us all at some point in time:) First two meetings will be presented by Mihaela. We will each teach two consecutive meetings. <br />
<br />
<span style="color:blue">UPDATE (09/17/2020): e met and all the documents (problems discussed and solutions given by you in class, are now shared with you via onedrive (app related to your outlook wisc account!)). I have also sent to you an invitation to use the witheboard attached to the same wisc account! But, do not feel discouraged in case you want to join later! You are always welcomed! </span><br />
<br />
<span style="color:green"> Please check out the following book: '''Putnam and Beyond'''! We will use it throughout the meetings!</span><br />
<br />
The first list of problems is posted! Please email me if you want access to it! [[File:Putnam_Problem_Set_1.pdf ]]<br />
<br />
<br />
|-<br />
|Meeting 23 SEPT 2020<br />
Mihaela Ifrim <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We discussed the problems given in the Putnam_Problem_Set_1 and their solutions are now posted on the shared folder.<br />
In addition I have also gave you the following problems to think at. [[File:Putnam_September_23_2020.pdf]]</span> <br />
<br />
<br />
<br />
<br />
|-<br />
|Meeting 30 SEPT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please consider joining ! <br />
<span style="color:Indigo">The next meeting will cover NUMBER THEORY! Please see the attached list of problems!! Enjoy!!! [[File:Putnam_nt1(1).pdf ]]</span><br />
<br />
<br />
<br />
|-<br />
|Meeting 7 OCT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam_nt2.pdf]] If you have solutions for the previous proposed set of problems, please email them so that we can compile a set of solutions. We will post them in our onedrive folder. If you are new, please email us and we will give access to it!<br />
|-<br />
<br />
-<br />
|Meeting 14 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] A more detailed list is posted on onedrive! <br />
|-<br />
<br />
-<br />
|Meeting 21 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! We worked out some of the problem proposed on the previous meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] Some solutions will be posted on onedrive! Reach out to us if you would like access to the solutions and you did not register yet! <br />
|-<br />
-<br />
|Meeting 28 OCT 2020<br />
Tatyana Shcherbina <br />
<br />
| ZOOM: Please join! The next two meeting will cover '''Polynomials'''! Please see the attached list of problems!! Enjoy!!! [[File: putnam_pol1.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the theory discussed on Oct 28 and hints to the problems [[File: putnam_pol1_hints.pdf ]] and [[File: polynomials_theory.pdf ]] <br />
|-<br />
<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the solutions of Polynomials problems [[File: putnam_Oct28_sol.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 11 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''Linear algebra'''. Here are the [[Media:linear_algebra_2020.pdf | problems]] I plan to discuss, and here is a short [http://math.northwestern.edu/putnam/filom/Linear_and_Abstract_Algebra.pdf summary] (from NWU) of some common linear algebra techniques for math contests.<br />
|-<br />
<br />
|Meeting 18 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). Continuing with the linear algebra: here are the [[Media:linear_algebra_2_2020.pdf | problems]] (including some left-overs from the last time). <br />
|-<br />
<br />
|Meeting 2 Dec 2020<br />
Botong Wang <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''limits of sequences''' (sections 3.1.3, 3.1.4, 3.1.5 in Putnam and Beyond). We will go over some basic theorems and discuss how to apply them. Here is the [[Media:Putnam_limits.pdf | worksheet]].<br />
|-<br />
|}<br />
<br />
<br />
----<br />
<br />
==Spring 2020==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. <br />
<br />
The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 5: [[Media:Putnam_Binomial2020.pdf | Binomial coefficients and generating functions]] [[Media:Putnam_Binomial2020_answer.pdf | (Answers and hints)]] Botong <br />
* February 19: [[Media:Putnam_Number_theory2020.pdf | Number theory]] [[Media:Putnam_Number2020.pdf | (Answers and hints)]] Botong<br />
* March 4 and 11: [[Media: Inequalities.pdf | Inequalities]] ( Note comming up!) Kim<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
* November 13: ??<br />
* November 20: [[Geometry.pdf | Geometry]] ( Note comming up!) Mihaela<br />
* November 27: [[No meeting! Thanksgiving! ]]<br />
* December 4: Last meeting of the semester! Please come and bring your friends too!! It will be fun! Mihaela<br />
<br />
<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other Olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=23075Putnam Club2022-04-06T16:42:49Z<p>Ifrim: </p>
<hr />
<div>==Spring 2022==<br />
<br />
[[File:Bascom-fall-1500x500-1500x500.jpg ]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2022 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatyana Shcherbina, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from February 2) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://hilbert.math.wisc.edu/wiki/index.php/Undergraduate_Math_Competition The sixth UW Madison undergraduate math competition] will take place on Saturday, April 23! The exact time and location will be announced soon. </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting February 2, 2022<br />
Dima Arinkin<br />
|Meeting at the 9th floor lounge Van Vleck. When: February 2, 2022 05:00 PM. <br />
<br />
[[Media:Putnam101415.pdf | Matrices and determinants]]<br />
<br />
|-<br />
|Meeting February 9, 2022<br />
Dima Arinkin<br />
| [[Media:Putnam020922.pdf | Functions and calculus]]<br />
<br />
|-<br />
|Meeting February 16, 2022<br />
Tatyana Shcherbina<br />
|We are going to discuss [[Media:PutClub_S22_an.pdf | Analysis problems]]<br />
<br />
|-<br />
|Meeting February 23, 2022<br />
Tatyana Shcherbina<br />
|We are going to continue to discuss [[Media:PutClub_S22_an2.pdf | Analysis problems 2]]<br />
<br />
|-<br />
|Meeting March 2, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_graph_theory_2022_Botong.pdf | Graph theory]]<br />
<br />
|-<br />
|Meeting March 9, 2022<br />
Botong Wang<br />
|We are going to discuss [[Media:Putnam_geometry_2022.pdf | Geometry]]<br />
<br />
|-<br />
|Meeting March 23, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam032322.pdf | Games]]<br />
<br />
|-<br />
|Meeting March 30, 2022<br />
Dima Arinkin<br />
| [[Media: Putnam033022.pdf | Generating functions and telescoping series]]<br />
<br />
|-<br />
|Meeting April 6, 2022<br />
Mihaela Ifrim<br />
| [Media: Competition_problems.pdf | Competition problems]]<br />
<br />
|-<br />
|Meeting April 13, 2022<br />
Mihaela Ifrim<br />
|<br />
<br />
|-<br />
|Meeting April 20, 2022<br />
Tatyana Shcherbina<br />
|<br />
<br />
|-<br />
|Meeting April 27, 2022<br />
Tatyana Shcherbina<br />
|<br />
|}<br />
</center><br />
<br />
[[File:WiscFall.jpg ]]<br />
<br />
==Fall 2021==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 22) at Van Vleck 9th floor lounge for some challenging questions, pizzas and drinks!!!'''<br />
<br />
<br />
<div style="text-align: center;"><span style="color:blue"><font size="3">[https://www.maa.org/math-competitions/putnam-competition The 82nd Putnam competition] will take place on Saturday, December 4, at Van Vleck B123 (we will move the afternoon exam to B3 floor, most likely B333, due to noise issues) (9AM-Noon, 2PM-5PM). Make sure to register for the competition!!!</font></span><br />
<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting September 22, 2021<br />
Botong Wang<br />
|Meeting at the 9th floor lounge Van Vleck. When: Sep 22, 2021 05:00 PM. <br />
<br />
In the first two lectures, we will take a look at some of the Putnam competition problems from [https://kskedlaya.org/putnam-archive/2020.pdf 2020] and [https://kskedlaya.org/putnam-archive/2019.pdf 2019]. <br />
<br />
We plan to start with algebraic problems such as 2019 A1, A2, B1, B3, 2020 A1, A2, B1. Then continue to the analytic ones such as 2019 A3, A4, B2, 2020 A3. <br />
<br />
|-<br />
|Meeting September 29th, 2021<br />
Botong Wang <br />
<br />
<br />
|Continue the two sets of Putnam problems from last time. <br />
<br />
|-<br />
|Meeting October 6th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Polynomials. We'll look at the [[Media:Putnam100621-Polynomials.pdf | following problems]] (the last few problems are quite hard, and we probably won't get to them during the meeting).<br />
<br />
|-<br />
|Meeting October 13th, 2021<br />
Dima Arinkin<br />
<br />
<br />
|Continuing with the problems from last time. If you have the time, please look at the problems in advance, and then if you have ideas or questions, we would talk about it at the start. <br />
<br />
|-<br />
|Meeting October 20th, 2021<br />
Tatyana<br />
<br />
| We are going to discuss number theory problems. The plan is to look on some of the [[Media:PutClub_F21_nt.pdf | following problems]] (we probably will not cover them all)<br />
<br />
<br />
|-<br />
|Meeting October 27th, 2021<br />
Tatyana<br />
<br />
|We will continue to discuss some number theory problems from the list<br />
<br />
|-<br />
|Meeting November 3rd, 2021<br />
Botong<br />
<br />
|We are going to discuss [[Media:Putnam_inequalities_2021.pdf | Inequalities!]] <br />
<br />
|-<br />
|Meeting November 10th, 2021<br />
Botong<br />
<br />
|We continue the discussion of inequalities<br />
<br />
|-<br />
|Meeting November 17th, 2021<br />
Mihaela Ifrim<br />
<br />
|We started discussing [[Media:Putnam 11.24.2021.pdf | Various problems from past competitions]] <br />
<br />
<br />
|-<br />
|Meeting November 24th, 2021<br />
<br />
<br />
|Thanksgiving break<br />
<br />
|<br />
<br />
|-<br />
|Meeting December 1st, 2021<br />
Mihaela Ifrim<br />
<br />
|Working in the extra problems added to the Nov 17th pdf. Solutions to all the problems: [[Media:Putnam_11.22.2021_Sols.pdf | Various problems from past competitions]] <br />
<br />
|-<br />
|Meeting December 8th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the actual Putnam problems. Covered half of them.<br />
<br />
<br />
<br />
|-<br />
|Meeting December 15th, 2021<br />
Mihaela Ifrim<br />
<br />
|Worked on the remaining problems; we still have some left: A6 and B5. See you all after the Winter break!<br />
<br />
<br />
<br />
|}<br />
</center><br />
<br />
<br />
<br />
<br />
==Spring 2021==<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE SPRING 2021 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. In a regular year is given on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3-hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
Due to the coronavirus crisis, '''the 81st Putnam Competition''', originally scheduled for Fall 2020, has been postponed until Feb. 20, 2021. The competition was in an '''unofficial mode''', with no proctors, no prizes, no awards, and no national recognition of high-scoring individuals or teams. The solution papers are uploaded by participants for grading. Scores will be reported back privately to the individual participants and the local supervisor of each institution will receive a report of the scores of the students for that institution. <br />
<br />
'''We will not continue our Putnam club meetings after March 24. See you all in the fall!<br />
'''<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting Feb 10, 2021<br />
Botong Wang<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Feb 10, 2021 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJMrd-yhpjstHt34UK8YJ9_mZJ7NT_G3NLcM After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
The first two meetings will be presented by Botong. We will look at some of the most recent Putnam exams to help you prepare for the coming one. <br />
<br />
On Feb 10, we will go over some of the [https://www.maa.org/sites/default/files/pdf/Putnam/2019/2019PutnamProblems.pdf 2019 Putnam problems]. <br />
<br />
|-<br />
|Meeting Feb 17, 2021<br />
Botong Wang <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will continue to discuss problems in the 2019 Putnam competition. We will also look at some of the [https://kskedlaya.org/putnam-archive/2018.pdf 2018 Putnam problems]. </span> <br />
<br />
<br />
|-<br />
|Meeting Feb 24, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We will look at some of the problems from [https://kskedlaya.org/putnam-archive/2020.pdf this year's Putnam] (which took place last weekend). </span> <br />
<br />
|-<br />
|Meeting Mar 3, 2021<br />
Dima Arinkin<br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">Let's keep looking at the [https://kskedlaya.org/putnam-archive/2020.pdf Putnam problems] - some interesting ones left!</span> <br />
<br />
|-<br />
|Meeting Mar 10 and Mar 17, 2021<br />
Botong Wang<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will discuss several apects of combinatorics: graphs, set theory and geometric combinatorics. The worksheet is [[Media: Putnam_Combinatorics_2021.pdf | here]].</span> <br />
|<br />
<br />
|-<br />
|Meeting Mar 24, 2021<br />
Mihaela Ifrim<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">This week we will go over problems in linear algebra and analysis. The worksheet is [[Media: Putnam-Problems_and_Theory_form_March_23_2021.pdf | here]].</span><br />
|}<br />
<br />
<br />
<br />
==Fall 2020==<br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE FALL 2020 PUTNAM CLUB!</div></font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Dima Arinkin, Mihaela Ifrim, Tatiana Shcherbyna, Botong Wang </font></span><br />
<br />
<br />
<div style="text-align: center;"><span style="color:crimson">However, this year things are a bit unusual. The 2020 Putnam competition is postponed until February 20, 2021. It is not determined yet whether the competition will be in person or online yet.Here is the original statement on the official webpage of the contest:</span> </div><br />
<br />
''Due to the coronavirus crisis, most students in the US and Canada are unable to return to campuses this fall. Therefore, the 81st Putnam Competition, originally scheduled for Fall 2020, will be postponed until February 20, 2021. If most students can return to campuses in the spring, the competition on that date can go forward in much the same form as in previous years. On the other hand, if most students are unable to return to campuses in the spring, the competition on that date will proceed in an unofficial mode, with no proctors, no prizes, no awards, but with solution papers submitted for grading by participants themselves and scores reported back privately to the individual participants.<br />
<br />
''<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;">[http://kskedlaya.org/putnam-archive/ <font size="3">Old exams and more information on the Putnam competition.</font>]</div></div><br />
<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://intranet.math.vt.edu/people/plinnell/Vtregional/ <span style="color:crimson"> over here.</div>] <br />
<br />
<div style="text-align: center;"><font size="3">'''We will have online meetings every Wednesday 5:00-6:30PM. ''' </font></div><br />
<br />
<br />
<div style="text-align: center;"><div style="background-color:pink;"> <font size="3">The first meeting of this semester will happen on the 16th of September 2020! Please let all your colleagues know that we are continuing the Putnam Club and we are enthusiastic and hopeful we will keep you all engaged throughout the semester!</font> </div></div><br />
<br />
<br />
{| class="wikitable" style="color:red; background-color:#ffffcc;" cellpadding="50"<br />
|Meeting 16 SEPT 2020<br />
Mihaela Ifrim<br />
|ZOOM MEETING: Hi there, You are invited to a Zoom meeting. <br />
When: Sep 16, 2020 05:00 PM Central Time (US and Canada) <br />
<br />
Register in advance for this meeting:<br />
https://uwmadison.zoom.us/meeting/register/tJApcumhrz4pEtJRe_o0WTGM26u2zTM8T6J5 After registering, you will receive a confirmation email containing information about joining the meeting.<br />
<br />
You will meet us all at some point in time:) First two meetings will be presented by Mihaela. We will each teach two consecutive meetings. <br />
<br />
<span style="color:blue">UPDATE (09/17/2020): e met and all the documents (problems discussed and solutions given by you in class, are now shared with you via onedrive (app related to your outlook wisc account!)). I have also sent to you an invitation to use the witheboard attached to the same wisc account! But, do not feel discouraged in case you want to join later! You are always welcomed! </span><br />
<br />
<span style="color:green"> Please check out the following book: '''Putnam and Beyond'''! We will use it throughout the meetings!</span><br />
<br />
The first list of problems is posted! Please email me if you want access to it! [[File:Putnam_Problem_Set_1.pdf ]]<br />
<br />
<br />
|-<br />
|Meeting 23 SEPT 2020<br />
Mihaela Ifrim <br />
<br />
<br />
| Zoom: Please join using the above link!<br />
<span style="color:Indigo">We discussed the problems given in the Putnam_Problem_Set_1 and their solutions are now posted on the shared folder.<br />
In addition I have also gave you the following problems to think at. [[File:Putnam_September_23_2020.pdf]]</span> <br />
<br />
<br />
<br />
<br />
|-<br />
|Meeting 30 SEPT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please consider joining ! <br />
<span style="color:Indigo">The next meeting will cover NUMBER THEORY! Please see the attached list of problems!! Enjoy!!! [[File:Putnam_nt1(1).pdf ]]</span><br />
<br />
<br />
<br />
|-<br />
|Meeting 7 OCT 2020<br />
Tatyana Shcherbyna <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam_nt2.pdf]] If you have solutions for the previous proposed set of problems, please email them so that we can compile a set of solutions. We will post them in our onedrive folder. If you are new, please email us and we will give access to it!<br />
|-<br />
<br />
-<br />
|Meeting 14 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! Here is the list of problems for the next meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] A more detailed list is posted on onedrive! <br />
|-<br />
<br />
-<br />
|Meeting 21 OCT 2020<br />
Mihaela Ifrim <br />
<br />
| ZOOM: Please join! We worked out some of the problem proposed on the previous meeting!!! [[File:Putnam-Problems-and-Theory-form-Oct-14th-2020-short.pdf ]] Some solutions will be posted on onedrive! Reach out to us if you would like access to the solutions and you did not register yet! <br />
|-<br />
-<br />
|Meeting 28 OCT 2020<br />
Tatyana Shcherbina <br />
<br />
| ZOOM: Please join! The next two meeting will cover '''Polynomials'''! Please see the attached list of problems!! Enjoy!!! [[File: putnam_pol1.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the theory discussed on Oct 28 and hints to the problems [[File: putnam_pol1_hints.pdf ]] and [[File: polynomials_theory.pdf ]] <br />
|-<br />
<br />
<br />
<br />
|Meeting 4 Nov 2020<br />
Tatyana Shcherbina <br />
<br />
| Here are the solutions of Polynomials problems [[File: putnam_Oct28_sol.pdf ]] <br />
|-<br />
<br />
<br />
|Meeting 11 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''Linear algebra'''. Here are the [[Media:linear_algebra_2020.pdf | problems]] I plan to discuss, and here is a short [http://math.northwestern.edu/putnam/filom/Linear_and_Abstract_Algebra.pdf summary] (from NWU) of some common linear algebra techniques for math contests.<br />
|-<br />
<br />
|Meeting 18 Nov 2020<br />
Dima Arinkin <br />
<br />
| On ZOOM (the link is above). Continuing with the linear algebra: here are the [[Media:linear_algebra_2_2020.pdf | problems]] (including some left-overs from the last time). <br />
|-<br />
<br />
|Meeting 2 Dec 2020<br />
Botong Wang <br />
<br />
| On ZOOM (the link is above). The topic for the next two meetings is '''limits of sequences''' (sections 3.1.3, 3.1.4, 3.1.5 in Putnam and Beyond). We will go over some basic theorems and discuss how to apply them. Here is the [[Media:Putnam_limits.pdf | worksheet]].<br />
|-<br />
|}<br />
<br />
<br />
----<br />
<br />
==Spring 2020==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. <br />
<br />
The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 5: [[Media:Putnam_Binomial2020.pdf | Binomial coefficients and generating functions]] [[Media:Putnam_Binomial2020_answer.pdf | (Answers and hints)]] Botong <br />
* February 19: [[Media:Putnam_Number_theory2020.pdf | Number theory]] [[Media:Putnam_Number2020.pdf | (Answers and hints)]] Botong<br />
* March 4 and 11: [[Media: Inequalities.pdf | Inequalities]] ( Note comming up!) Kim<br />
<br />
==Fall 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 25th of September in Van Vleck hall, room B139.'''<br />
<br />
We will continue using the [http://piazza.com/wisc/fall2018/putnam2018/ Piazza page] from last semester for discussions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* September 25: [[Media:Putnam_problems_2017+2018.pdf | Introductory meeting]] Botong<br />
* October 2: [[Putnam.pdf | Integral inequalities]] Mihaela<br />
* October 9: [[Putnam.pdf | More about Integral inequalities]] (I will post notes on Wednesday morning and we will discuss more in class!) Mihaela<br />
* October 16: [[ODE.pdf | ODE of the first order]] Chanwoo<br />
* November 6: [[Media:Numbers.pdf | Number theory]] Dima<br />
* November 13: ??<br />
* November 20: [[Geometry.pdf | Geometry]] ( Note comming up!) Mihaela<br />
* November 27: [[No meeting! Thanksgiving! ]]<br />
* December 4: Last meeting of the semester! Please come and bring your friends too!! It will be fun! Mihaela<br />
<br />
<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other Olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. The first meeting will be on the 6th of February in Van Vleck hall, room B139.<br />
<br />
<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=File:Competition_problems.pdf&diff=23074File:Competition problems.pdf2022-04-06T16:42:11Z<p>Ifrim: </p>
<hr />
<div></div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23068PDE Geometric Analysis seminar2022-04-05T00:25:15Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: in person, Room: 901, Time: 3:30PM -4:30PM<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23067PDE Geometric Analysis seminar2022-04-05T00:24:28Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: in person, Room: 901, Time: 3:30PM -4:30PM<br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[TBA]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23057PDE Geometric Analysis seminar2022-04-02T18:35:31Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room: 901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: in person, Room:--, Time:-- <br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[TBA]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation and strong stratification. When incorporating the dynamics of water content in the atmosphere, a.k.a. moisture, one may then study the moist Boussinesq equations and its limit, the precipitating quasi-geostrophic equations.<br />
<br />
These models are important for atmospheric scientists in light of the role that the water cycle plays in atmospheric dynamics, notably through energy budgeting (such as for example when atmospheric circulations are driven by laten heat release in storms). Mathematically, these models present interesting challenges due to the presence of boundaries, whose locations are a priori unknown, between phases saturated and unsaturated in water (schematically: boundaries between clouds and their surroundings).<br />
<br />
In particular, while the (dry) quasi-geostrophic equations rely on the inversion of a Laplacian, this becomes a much trickier adversary in the presence of free boundaries. In this talk we will discuss how this nonlinear equation underpinning the precipitating quasi-geostrophic equations can be characterized using a variational formulation and we will describe the many benefits one may derive from this formulation.<br />
<br />
<br />
'''October 11th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''October 18th, 2021.'''<br />
<br />
[[Wojciech Ozanski]] (USC); Format: online seminar via Zoom, Room:--, Time: 3:30PM-4:30PM<br />
<br />
Title: Well-posedness of logarithmic spiral vortex sheets.<br />
<br />
Abstract: We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.<br />
<br />
<br />
'''October 25th, 2021.'''<br />
<br />
[[Maxwell Stolarski]] (ASU); Format: in person seminar, Room: 901, Time: 3:30pm-4:30pm<br />
<br />
Title: Mean Curvature Flow Singularities with Bounded Mean Curvature<br />
<br />
Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be smoothly extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity<br />
<br />
Abstract: This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: Well-posedness for the dispersion-generalized Benjamin-Ono equation<br />
<br />
Abstract: In this talk we will consider the Cauchy problem for both low and high dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we use a pseudodifferential generalization of the gauge transform introduced by Tao for the original Benjamin-Ono equation. Further, we combine this with a paradifferential normal form. This approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, [[Time:10 AM]] <br />
<br />
[[Please observe the time change! ]]<br />
<br />
Zoom Link: Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP<br />
<br />
<br />
Title: Global wellposedness for the energy-critical Zakharov system below the ground state<br />
<br />
Abstract: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\"odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
[[No seminar]]<br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
[[William Cooperman]] (University of Chicago); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
Title: Quantitative homogenization of Hamilton-Jacobi equations<br />
<br />
Abstract: We are interested in the rate at which solutions to a Hamilton-Jacobi equation converge, in the large-scale limit, to the solution of the effective problem. We'll describe prior work in various settings where homogenization occurs (periodic or random in space, coercive or only "coercive on average" in momentum as in the G equation). We'll also use a theorem of Alexander, originally proved in the context of first-passage percolation, to improve the rate of convergence when an optimal control formulation is available (for example, in the G equation or when the Hamiltonian is convex and coercive).<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
<br />
[[No seminar ]]<br />
<br />
<br />
<br />
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==<br />
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. <br />
<br />
'''Week 1 (9/1/2020-9/5/2020)'''<br />
<br />
1. Paul Rabinowitz - The calculus of variations and phase transition problems.<br />
https://www.youtube.com/watch?v=vs3rd8RPosA<br />
<br />
2. Frank Merle - On the implosion of a three dimensional compressible fluid.<br />
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be <br />
<br />
'''Week 2 (9/6/2020-9/12/2020)'''<br />
<br />
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.<br />
https://www.youtube.com/watch?v=4ndtUh38AU0<br />
<br />
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI<br />
<br />
<br />
<br />
'''Week 3 (9/13/2020-9/19/2020)'''<br />
<br />
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ<br />
<br />
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE<br />
<br />
<br />
<br />
'''Week 4 (9/20/2020-9/26/2020)'''<br />
<br />
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be<br />
<br />
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM<br />
<br />
<br />
<br />
'''Week 5 (9/27/2020-10/03/2020)'''<br />
<br />
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo<br />
<br />
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c<br />
<br />
<br />
'''Week 6 (10/04/2020-10/10/2020)'''<br />
<br />
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E<br />
<br />
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing<br />
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html<br />
<br />
<br />
'''Week 7 (10/11/2020-10/17/2020)'''<br />
<br />
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s<br />
<br />
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg<br />
<br />
<br />
'''Week 8 (10/18/2020-10/24/2020)'''<br />
<br />
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg<br />
<br />
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ<br />
<br />
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.<br />
<br />
<br />
'''Week 9 (10/25/2020-10/31/2020)'''<br />
<br />
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE<br />
<br />
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764<br />
<br />
<br />
<br />
'''Week 10 (11/1/2020-11/7/2020)'''<br />
<br />
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be<br />
<br />
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html<br />
<br />
<br />
<br />
'''Week 11 (11/8/2020-11/14/2020)'''<br />
<br />
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc<br />
<br />
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0<br />
<br />
<br />
'''Week 12 (11/15/2020-11/21/2020)'''<br />
<br />
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY<br />
<br />
2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk<br />
<br />
<br />
'''Week 13 (11/22/2020-11/28/2020)'''<br />
<br />
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be<br />
<br />
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8<br />
<br />
'''Week 14 (11/29/2020-12/5/2020)'''<br />
<br />
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, <br />
https://youtu.be/xfAKGc0IEUw<br />
<br />
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc<br />
<br />
<br />
<br />
'''Week 15 (12/6/2020-12/12/2020)'''<br />
<br />
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be<br />
<br />
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU<br />
<br />
<br />
'''Spring 2021'''<br />
<br />
'''Week 1 (1/31/2021- 2/6/2021)'''<br />
<br />
1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be<br />
<br />
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84<br />
<br />
<br />
'''Week 2 ( 2/7/2021- 2/13/2021)'''<br />
<br />
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek<br />
<br />
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE<br />
<br />
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.<br />
<br />
'''Week 3 ( 2/14/2021- 2/20/2021)'''<br />
<br />
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s<br />
<br />
2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg<br />
<br />
<br />
<br />
'''Week 4 ( 2/21/2021- 2/27/2021)'''<br />
<br />
1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309<br />
<br />
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68<br />
<br />
'''Week 5 ( 2/28/2021- 3/6/2021)'''<br />
<br />
1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317<br />
<br />
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k<br />
<br />
'''Week 6 (3/7/2021-3/13/2021)'''<br />
<br />
1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html<br />
<br />
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c<br />
<br />
<br />
'''Week 7 (3/14/2021-3/20/2021)'''<br />
<br />
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM<br />
<br />
2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html<br />
<br />
<br />
<br />
'''Week 8 (3/21/2021- 3/27/2021)'''<br />
<br />
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs<br />
<br />
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A<br />
<br />
<br />
<br />
'''Week 9 (3/28/2021- 4/3/2021)'''<br />
<br />
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM<br />
<br />
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9<br />
<br />
<br />
'''Week 10 (4/4/2021- 4/10/2021)'''<br />
<br />
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235<br />
<br />
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8<br />
<br />
'''Week 11(4/11/2021- 4/17/2021)'''<br />
<br />
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo<br />
<br />
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html<br />
<br />
'''Week 12(4/18/2021- 4/24/2021)'''<br />
<br />
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0<br />
<br />
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo<br />
<br />
'''Week 13(4/25/2021- 5/1/2021)'''<br />
<br />
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI <br />
<br />
2. Stefania Patrizi - Chaotic Orbits for systems of nonlocal equations http://www.birs.ca/events/2017/5-day-workshops/17w5116/videos/watch/201704050939-Patrizi.html<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|- <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Ifrimhttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23056PDE Geometric Analysis seminar2022-04-02T18:34:06Z<p>Ifrim: </p>
<hr />
<div>The seminar's format will be a combination of online and in-person; we will make sure to update you as soon as we have more details available. First talk is tentatively scheduled for September 20th ! <br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
===[[Fall 2021-Spring 2022 | Schedule for Fall 2021-Spring 2022]]===<br />
<br />
Some of the seminars will be held online. When that would be the case we would use the following zoom link<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[No Seminar]]<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[Jonah Duncan]] from John Hopkins University ; Format: online seminar via Zoom (see link above), Time: 3:30-4:30PM <br />
<br />
Title: Estimates and regularity for the k-Yamabe equation <br />
<br />
Abstract: The k-Yamabe problem is a fully nonlinear generalisation of the Yamabe problem, concerned with finding conformal metrics with constant k-curvature. In this talk, I will start by introducing the k-Yamabe problem, including a brief survey of established results and open problems. I will then discuss some recent work (joint with Luc Nguyen) on estimates and regularity for the k-Yamabe equation, addressing solutions in both the so-called positive and negative cones.<br />
<br />
<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
<br />
Title: MCF after the Velázquez&mdash;Stolarski example.<br />
<br />
Abstract: Velázquez (1995) constructed an example of a Mean Curvature Flow $M_t\subset\mathbb R^8$, $(-1<t<0)$ that blows up at the origin as $t\nearrow0$.<br />
Stolarski recently showed that in spite of the singularity the mean curvature on this solution is uniformly bounded. <br />
In joint work with Daskalopoulos and Sesum we constructed an extension of the Velázquez&mdash;Stolarski solution to positive times and show that it also has uniformly bounded mean curvature. In the talk I will describe the solutions and explain some of the ideas that show boundedness of the mean curvature.<br />
<br />
<br />
<br />
'''February 21th, 2022.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time: 11:00 AM<br />
<br />
Title: Nontrivial self-similar blowup in energy supercritical nonlinear wave equations<br />
<br />
Abstract: Self-similar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finite-time blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new non-trivial self-similar solutions, which are completely explicit in all supercritical dimensions. Furthermore, we outline methods to analyse their stability. This involves a delicate spectral problem that we are able to solve rigorously in particular space dimensions. In these cases, we prove that the solutions are co-dimension one stable modulo translations. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck). <br />
<br />
<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Time:3:30PM-4:30PM<br />
<br />
Title: On quantum Boltzmann fluctuation dynamics at the presence of a BEC<br />
<br />
Abstract: Boltzmann equations have served to describe transport properties in many instances. While usually heuristically justified by means of Markov processes, mathematically rigorous derivations from first principles started arising with the landmark works of Lanford and Cercignani, and there have been many important improvements ever since. To this day, it remains a very active mathematical and physical field. Starting with the Liouville-von Neumann equation for a weakly interacting highly condensed Bose gas in a finite periodic box, we will uncover a Boltzmann dynamics after identifying other dominating effects. Our work exhibits some parallels with a previous discussion by Zaremba-Niguni-Griffin. However, we will present an analytic dependence on physical parameters for the size of the individual terms in the expansion, for the size of errors, for the time of validity, as well as among physical parameters. We will also see how mathematical rigor uncovers important physical subtleties missed in the physical literature. Our work is the first rigorous derivation of a quantum Boltzmann equation from first principles. This is a joint work with Thomas Chen.<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; <br />
<br />
<br />
<br />
<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<br />
<br />
<br />
<br />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time: 3:30PM-4:30PM<br />
<br />
https://uwmadison.zoom.us/j/96354681353?pwd=SGlwUW1ockp6YklYYlppbDFZcW8zdz09<br />
<br />
Meeting ID: 963 5468 1353<br />
Passcode: 180680<br />
<br />
Title: Determinants, commuting flows, and recent progress on<br />
completely integrable systems<br />
<br />
Abstract: I will survey a number of recent developments in the theory<br />
of completely integrable nonlinear dispersive PDE. These include a<br />
priori bounds, the orbital stability of multisoliton solutions,<br />
well-posedness at optimal regularity, and the existence of dynamics<br />
for Gibbs distributed initial data. I will describe the basic objects<br />
that tie together these disparate results, as well as the diverse<br />
ideas required for each problem.<br />
<br />
<br />
'''April 4th, 2022.'''<br />
<br />
[[Marcelo Disconzi]]; Format: online seminar via Zoom/ in person, Room:901, Time: 3:30PM <br />
<br />
Title: General-relativistic viscous fluids.<br />
<br />
<br />
Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has<br />
<br />
intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.<br />
<br />
<br />
<br />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: in person, Room:--, Time:-- <br />
<br />
Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations<br />
<br />
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo<br />
<br />
<br />
<br />
'''April 18th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[TBA]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
<br />
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness<br />
<br />
Abstract: In this talk, I will present some recent results obtained in<br />
collaboration with V. Patel (Oxford) in connection with a system<br />
describing a heat-conducting incompressible fluid. I will introduce the<br />
notion of a dissipative weak solution of the system and highlight the<br />
connections and differences to the existing approaches in the<br />
literature. One of the advantages of the proposed approach is that the<br />
solution satisfies a weak-strong uniqueness principle, which guarantees<br />
that the weak solution will coincide with the strong solution, as long<br />
as the latter exists; moreover, the solutions are constructed via a<br />
finite element approximation, leading (almost, not quite) to the first<br />
convergence result for the full system including viscous dissipation.<br />
<br />
<br />
<br />
=Fall 2021=<br />
<br />
'''September 20th, 2021.'''<br />
<br />
[[Simion Schulz]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
<br />
Title: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts<br />
<br />
Abstract: We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally derived from a large particle system and models the evolution of an arbitrary number of (e.g. biological) species with quadratic porous medium interactions in a bounded domain of arbitrary dimension. The cross-interactions are scaled by a coefficient on which a necessary smallness condition is imposed. The strategy of our proof relies on a fixed point argument, followed by a vanishing viscosity scheme. This is joint work with Maria Bruna (Cambridge), Luca Alasio (Paris VI), and Simone Fagioli (Università degli Studi dell'Aquila).<br />
<br />
<br />
<br />
'''September 27th, 2021.'''<br />
<br />
[[Dohyun Kwon]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Volume-preserving crystalline and anisotropic mean curvature flow<br />
<br />
Abstract: We consider the global existence of volume-preserving crystalline mean curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address the global existence and regularity of the flow for smooth anisotropies. For the non-smooth case, we establish global existence results for the types of anisotropies known to be globally well-posed. This is joint work with Inwon Kim (UCLA) and Norbert Požár (Kanazawa University).<br />
<br />
<br />
'''October 4th, 2021.'''<br />
<br />
[[Antoine Remind-Tiedrez]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: Variational formulation, well-posedness, and iterative methods for moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries<br />
<br />
Abstract: To describe the atmosphere on a synoptic scale (the scale at which high- and low-pressure systems are apparent on a weather map, for example) one may use the quasi-geostrophic equations, which are derived as a limit of the classical Boussinesq system under the assumptions of fast rotation a