https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Angenent&feedformat=atomUW-Math Wiki - User contributions [en]2023-06-05T23:03:19ZUser contributionsMediaWiki 1.39.3https://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=24365PDE Geometric Analysis seminar2023-02-02T21:22:11Z<p>Angenent: added Zhihan Wang on April 3</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 />
<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 />
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<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 />
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<br />
<br />
== PDE GA Seminar Schedule Fall 2022-Spring 2023 ==<br />
<br />
=Spring 2023= <br />
<br />
<br />
<br />
'''January 30, 2023 '''<br />
<br />
[[Jingwen Chen|Jingwen Chen]] (U Chicago)<br />
<br />
Time: 3:30 PM -4:30 PM, in person in VV901 <br />
<br />
Title: Mean curvature flows in the sphere via phase transitions.<br />
<br />
Abstract: In this talk, we will discuss some solutions of the mean curvature flow (MCF) of surfaces in the 3-sphere. We will recall a generalized notion of MCF introduced by Brakke in the 70s, as well as its regularization by a parabolic partial differential equation arising in the theory of phase transitions. We will talk about some existence problems for this parabolic equation, and use them to construct MCFs that join minimal surfaces of low area in the 3-sphere, and some recent progress on the spaces of MCFs using Morse-Bott theory. <br />
<br />
This is joint work with Pedro Gaspar (Pontificia Universidad Católica de Chile). <br />
<br />
<br />
<br />
'''February 6, 2023'''<br />
<br />
[[TBA| TBA]] <br />
<br />
Format: , Time: <br />
<br />
'''Title:'''<br />
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'''Abstract:''' <br />
<br />
<br />
<br />
'''February 13, 2023'''<br />
<br />
Trinh Tien Nguyen (UW Madison) <br />
<br />
Format: In person, Time: 3:30-4:30PM. <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
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'''February 20, 2023'''<br />
<br />
[[Ovidiu Avadanei| Ovidiu Avadanei]] <br />
<br />
Format: , Time: <br />
<br />
'''Title:''' <br />
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'''Abstract:'''<br />
<br />
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<br />
'''February 27, 2023'''<br />
<br />
Yuxi Han (UW Madison) <br />
<br />
Format: In person, Time: 3:30-4:30PM. <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
<br />
<br />
<br />
<br />
'''March 6, 2023'''<br />
<br />
Jinwoo Jang (Postech), Host: Chanwoo Kim <br />
<br />
Format: In-person, Time: 3:30-4:30PM. <br />
<br />
'''Title:''' Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus <br />
<br />
'''Abstract:''' This talk deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the Vlasov-Maxwell system in a two-dimensional annulus when a huge (but finite-in-time) external magnetic potential is imposed near the boundary. We assume that the solution is axisymmetric. The external magnetic potential well that we impose remains finite within a finite time interval and from that, we prove that the plasma never touches the boundary. In addition, we provide a sufficient condition on the magnitude of the external magnetic potential to guarantee that the plasma is confined in an annulus of the desired thickness which is slightly larger than the initial support. Our method uses the cylindrical coordinate forms of the Vlasov-Maxwell system. This is a joint-work with Robert M. Strain and Tak Kwong Wong.<br />
<br />
<br />
<br />
'''March 13, 2023'''<br />
<br />
[[Spring Recess: No Seminar]] <br />
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<br />
<br />
'''March 20, 2023'''<br />
<br />
Gi-Chan Bae (Seoul Nat. University), Host: Chanwoo Kim <br />
<br />
Format: In-person, Time: 3:30-4:30PM. <br />
<br />
'''Title:''' <br />
<br />
'''Abstract:'''<br />
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<br />
'''March 27, 2023'''<br />
<br />
[[Yuan Gao|Matt Jacobs]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
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'''April 3, 2023'''<br />
<br />
Zhihan Wang (Princeton). Host: Sigurd Angenent <br />
<br />
Format: In person, Time: 3:30-4:30PM. <br />
<br />
'''Title:''' ''Translating mean curvature flow with simple end.''<br />
<br />
'''Abstract:''' Translators are known as candidates of Type II blow-up model for mean curvature flows. Various examples of mean curvature flow translators have been constructed in the convex case and semi-graphical case, most of which have either infinite entropy or higher multiplicity asymptotics near infinity. In this talk, we shall present the construction of a new family of translators with prescribed end. This is based on joint work with Ao Sun.<br />
<br />
<br />
<br />
'''April 10, 2023'''<br />
<br />
[[TBA| 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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'''April 17, 2023'''<br />
<br />
[[Jingrui Cheng]] (Stony Brook). Host: Misha Feldman.<br />
<br />
Format: , Time: <br />
<br />
'''Title:''' <br />
<br />
'''Abstract:'''<br />
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'''April 24, 2023'''<br />
<br />
[[Ben Pineau| Ben Pineau]] <br />
<br />
<br />
Format: , Time: <br />
<br />
'''Title:''' <br />
<br />
'''Abstract:'''<br />
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<br />
'''May 1, 2023'''<br />
<br />
[[TBA| 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 2022= <br />
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<br />
'''September 12, 2022'''<br />
<br />
[[No Seminar]]<br />
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<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 />
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<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 />
<br />
<br />
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<br />
'''October 3, 2022'''<br />
<br />
[[No Seminar]]<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 />
<br />
[[Alexander Kiselev]] (Duke). Host: Sergey Denisov.<br />
<br />
Date/time/place: Monday, October 10, 3:30-4:30 pm, VV 901 (if more space will be needed, we have VV B119 to migrate to).<br />
<br />
Speaker: Sasha Kiselev (Duke)<br />
<br />
Title: The flow of polynomial roots under differentiation<br />
Abstract: The question of how polynomial roots move under differentiation is classical. Contributions to this subject have been made by Gauss, Lucas, Marcel Riesz, Polya and many others. In 2018, Stefan Steinerberger derived formally a PDE that should describe the dynamics of roots under differentiation in certain situations. The PDE in question is of hydrodynamic type and bears a striking resemblance to the models used in mathematical biology to describe collective behavior and flocking of various species- such as fish, birds or ants. I will discuss joint work<br />
with Changhui Tan in which we establish global regularity of Steinerberger's equation and make a rigorous connection between its solutions and evolution of roots under differentiation for a class of trigonometric polynomials.<br />
<br />
<br />
<br />
'''October 17, 2022'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
'''Title:''' Analysis of adversarial robustness and of other problems in modern machine learning.<br />
<br />
'''Abstract:''' Modern machine learning methods, in particular deep learning approaches, have enjoyed unparalleled success in a variety of challenging application fields like image recognition, medical image reconstruction, and natural language processing. While a vast majority of previous research in machine learning mainly focused on constructing and understanding models with high predictive power, consensus has emerged that other properties like stability and robustness of models are of equal importance and in many applications essential. This has motivated researchers to investigate the problem of adversarial training (or how to make models robust to adversarial attacks), but despite the development of several computational strategies for adversarial training and some theoretical development in the broader distributionally robust optimization literature, there are still several theoretical questions about it that remain relatively unexplored. In this talk, I will take an analytical perspective on the adversarial robustness problem and explore three questions: 1)What is the connection between adversarial robustness and inverse problems?, 2) Can we use analytical tools to find lower bounds for adversarial robustness problems?, 3) How do we use modern tools from analysis and geometry to solve adversarial robustness problems? At its heart, this talk is an invitation to view adversarial machine learning through the lens of mathematical analysis, showcasing a variety of rich connections with perimeter minimization problems, optimal transport, mean field PDEs of interacting particle systems, and min-max games in spaces of measures. <br />
<br />
<br />
<br />
<br />
'''October 24, 2022'''<br />
<br />
[[No seminar.]]<br />
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Format: , Time: <br />
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Title:<br />
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Abstract:<br />
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<br />
'''October 31, 2022 '''<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures<br />
<br />
Abstract: We will give a gentle introduction of weak KAM theory and then reinterpret Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. We will use one-dimensional irreversible diffusion process on torus to illustrate some essential concepts in the weak KAM theory such as the Peierls barrier, the projected Mather/Aubry/Mane sets. We provide alternative proofs for Freidlin-Wentzell's variational formulas for both self-consistent boundary data at each local attractors and for the rate function are formulated as the global adjustment for the boundary data and the local trimming from the lifted Peierls barriers. Based on this, we proved the rate function is a weak KAM solution to the corresponding stationary Hamilton-Jacobi equation satisfying the selected boundary data on projected Aubry set, which is also the maximal Lipschitz continuous viscosity solution. The rate function is the selected unique weak KAM solution and also serves as the global energy landscape of the original stochastic process. A probability interpretation of the global energy landscape from the weak KAM perspective will also be discussed.<br />
<br />
<br />
<br />
'''November 7, 2022 '''<br />
<br />
[[Beomjun Choi]] (Postech)<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: Liouville theorem for surfaces translating by powers of Gauss curvature<br />
<br />
Abstract: We classify the entire solutions to degenerate Monge-Ampere equations $\det D^2u = (1+|Du|^2)^\beta$ on $\mathbb{R}^2$ for all $\beta<0$. The graphs of such solutions are the translating solitons to the flows by sub-affine-critical powers of Gauss curvature. In view of the Legendre transformation, this classifies the entire solutions to $\det D^2v = (1+|x|^2)^{-\beta}$ as well.<br />
<br />
For the affine-critical-case $\det D^2u =1$, the celebrated result by Jorgens, Calabi and Pogorelov shows every solution must be a convex paraboloid and hence the level sets are homothetic ellipses. In our case, the level sets of given solution converge to a circle or a curve with $k$-fold symmetry for some $k>2$. These curves are closed shrinking curves to the curve shortening flows, classified by B. Andrews in 2003. Then we study the moduli space of solutions for each prescribed asymptotics. This is a joint work with K. Choi and S. Kim.<br />
<br />
<br />
<br />
<br />
'''November 14, 2022 '''<br />
<br />
Adrian Tudorascu (West Virginia University). Host: Misha Feldman, Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: Sticky Particles with Sticky Boundary<br />
<br />
Abstract: We study the pressureless Euler system in an arbitrary closed subset of the real line. The reflective boundary condition renders an ill-posed problem. Instead, we show that the sticky boundary condition is natural and yields a well-posed problem which is treated by means of sticky particles solutions, Lagrangian solutions and an appropriate (and natural) reflection principle.<br />
<br />
<br />
<br />
<br />
<br />
'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: online <br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/94877483456?pwd=cG9Ec1dhb2ErcXhFVW1aN2hCYXRBUT09<br />
Meeting ID: 948 7748 3456<br />
Passcode: 303105<br />
<br />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: Sharp scattering results for the 3d cubic NLS<br />
<br />
Abstract: I will discuss several sharp scattering results for three-dimensional cubic nonlinear Schrödinger equations, including both the free NLS and the NLS with an external potential. After reviewing the proof of scattering below the mass/energy ground state threshold, I will discuss some work on scattering at the threshold for NLS with repulsive potentials. The talk will discuss joint works with B. Dodson; R. Killip, M. Visan, and J. Zheng; and C. Miao and J. Zheng.<br />
<br />
<br />
<br />
<br />
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<br />
'''November 28, 2022 '''<br />
<br />
[[No Seminar]]- Thanksgiving <br />
<br />
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<br />
<br />
<br />
'''December 5, 2022 '''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
<br />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: Solitary waves for infinite depth gravity water waves with constant vorticity<br />
<br />
Abstract: We show that solitary waves exist for pure gravity water waves in infinite depth in the presence of constant (nonzero) vorticity. The proof relies on the fact that this particular water-wave system is well-approximated by the Benjamin-Ono equation, which also allows a description of the profile of the solitary wave in terms of the Benjamin-Ono soliton. This is joint work with Lizhe Wan.<br />
<br />
<br />
<br />
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<br />
'''December 12, 2022 '''<br />
<br />
[[Calum Rickard ]] UC Davis<br />
<br />
Format: in-person in room VV901 <br />
<br />
Time: 3:00 PM -4:00 PM <br />
<br />
Title: An infinite class of shocks for compressible Euler<br />
<br />
Abstract: <br />
We consider the two dimensional compressible Euler equations with azimuthal symmetry and construct an infinite class of shocks by establishing shock formation for a new Hölder family of so-called pre-shocks for all nonnegative integers. Moreover, a precise description of the dominant Riemann variable in the Hölder space is given in the form of a fractional series expansion. This is joint work with Sameer Iyer, Steve Shkoller and Vlad Vicol.<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=24364PDE Geometric Analysis seminar2023-02-02T21:19:03Z<p>Angenent: </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 />
=Spring 2023= <br />
<br />
<br />
<br />
'''January 30, 2023 '''<br />
<br />
[[Jingwen Chen|Jingwen Chen]] (U Chicago)<br />
<br />
Time: 3:30 PM -4:30 PM, in person in VV901 <br />
<br />
Title: Mean curvature flows in the sphere via phase transitions.<br />
<br />
Abstract: In this talk, we will discuss some solutions of the mean curvature flow (MCF) of surfaces in the 3-sphere. We will recall a generalized notion of MCF introduced by Brakke in the 70s, as well as its regularization by a parabolic partial differential equation arising in the theory of phase transitions. We will talk about some existence problems for this parabolic equation, and use them to construct MCFs that join minimal surfaces of low area in the 3-sphere, and some recent progress on the spaces of MCFs using Morse-Bott theory. <br />
<br />
This is joint work with Pedro Gaspar (Pontificia Universidad Católica de Chile). <br />
<br />
<br />
<br />
'''February 6, 2023'''<br />
<br />
[[TBA| TBA]] <br />
<br />
Format: , Time: <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:''' <br />
<br />
<br />
<br />
'''February 13, 2023'''<br />
<br />
Trinh Tien Nguyen (UW Madison) <br />
<br />
Format: In person, Time: 3:30-4:30PM. <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
<br />
<br />
<br />
<br />
'''February 20, 2023'''<br />
<br />
[[Ovidiu Avadanei| Ovidiu Avadanei]] <br />
<br />
Format: , Time: <br />
<br />
'''Title:''' <br />
<br />
'''Abstract:'''<br />
<br />
<br />
<br />
'''February 27, 2023'''<br />
<br />
Yuxi Han (UW Madison) <br />
<br />
Format: In person, Time: 3:30-4:30PM. <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
<br />
<br />
<br />
<br />
'''March 6, 2023'''<br />
<br />
Jinwoo Jang (Postech), Host: Chanwoo Kim <br />
<br />
Format: In-person, Time: 3:30-4:30PM. <br />
<br />
'''Title:''' Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus <br />
<br />
'''Abstract:''' This talk deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the Vlasov-Maxwell system in a two-dimensional annulus when a huge (but finite-in-time) external magnetic potential is imposed near the boundary. We assume that the solution is axisymmetric. The external magnetic potential well that we impose remains finite within a finite time interval and from that, we prove that the plasma never touches the boundary. In addition, we provide a sufficient condition on the magnitude of the external magnetic potential to guarantee that the plasma is confined in an annulus of the desired thickness which is slightly larger than the initial support. Our method uses the cylindrical coordinate forms of the Vlasov-Maxwell system. This is a joint-work with Robert M. Strain and Tak Kwong Wong.<br />
<br />
<br />
<br />
'''March 13, 2023'''<br />
<br />
[[Spring Recess: No Seminar]] <br />
<br />
<br />
<br />
<br />
'''March 20, 2023'''<br />
<br />
Gi-Chan Bae (Seoul Nat. University), Host: Chanwoo Kim <br />
<br />
Format: In-person, Time: 3:30-4:30PM. <br />
<br />
'''Title:''' <br />
<br />
'''Abstract:'''<br />
<br />
<br />
'''March 27, 2023'''<br />
<br />
[[Yuan Gao|Matt Jacobs]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
<br />
<br />
'''April 3, 2023'''<br />
<br />
Zhihan Wang (Princeton). Host: Sigurd Angenent <br />
<br />
Format: , Time: <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
<br />
<br />
<br />
'''April 10, 2023'''<br />
<br />
[[TBA| TBA]] <br />
<br />
Format: , Time: <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
<br />
<br />
<br />
'''April 17, 2023'''<br />
<br />
[[Jingrui Cheng]] (Stony Brook). Host: Misha Feldman.<br />
<br />
Format: , Time: <br />
<br />
'''Title:''' <br />
<br />
'''Abstract:'''<br />
<br />
<br />
'''April 24, 2023'''<br />
<br />
[[Ben Pineau| Ben Pineau]] <br />
<br />
<br />
Format: , Time: <br />
<br />
'''Title:''' <br />
<br />
'''Abstract:'''<br />
<br />
<br />
<br />
'''May 1, 2023'''<br />
<br />
[[TBA| TBA]] <br />
<br />
Format: , Time: <br />
<br />
'''Title:'''<br />
<br />
'''Abstract:'''<br />
<br />
<br />
<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 />
[[No Seminar]]<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 />
Date/time/place: Monday, October 10, 3:30-4:30 pm, VV 901 (if more space will be needed, we have VV B119 to migrate to).<br />
<br />
Speaker: Sasha Kiselev (Duke)<br />
<br />
Title: The flow of polynomial roots under differentiation<br />
Abstract: The question of how polynomial roots move under differentiation is classical. Contributions to this subject have been made by Gauss, Lucas, Marcel Riesz, Polya and many others. In 2018, Stefan Steinerberger derived formally a PDE that should describe the dynamics of roots under differentiation in certain situations. The PDE in question is of hydrodynamic type and bears a striking resemblance to the models used in mathematical biology to describe collective behavior and flocking of various species- such as fish, birds or ants. I will discuss joint work<br />
with Changhui Tan in which we establish global regularity of Steinerberger's equation and make a rigorous connection between its solutions and evolution of roots under differentiation for a class of trigonometric polynomials.<br />
<br />
<br />
<br />
'''October 17, 2022'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
'''Title:''' Analysis of adversarial robustness and of other problems in modern machine learning.<br />
<br />
'''Abstract:''' Modern machine learning methods, in particular deep learning approaches, have enjoyed unparalleled success in a variety of challenging application fields like image recognition, medical image reconstruction, and natural language processing. While a vast majority of previous research in machine learning mainly focused on constructing and understanding models with high predictive power, consensus has emerged that other properties like stability and robustness of models are of equal importance and in many applications essential. This has motivated researchers to investigate the problem of adversarial training (or how to make models robust to adversarial attacks), but despite the development of several computational strategies for adversarial training and some theoretical development in the broader distributionally robust optimization literature, there are still several theoretical questions about it that remain relatively unexplored. In this talk, I will take an analytical perspective on the adversarial robustness problem and explore three questions: 1)What is the connection between adversarial robustness and inverse problems?, 2) Can we use analytical tools to find lower bounds for adversarial robustness problems?, 3) How do we use modern tools from analysis and geometry to solve adversarial robustness problems? At its heart, this talk is an invitation to view adversarial machine learning through the lens of mathematical analysis, showcasing a variety of rich connections with perimeter minimization problems, optimal transport, mean field PDEs of interacting particle systems, and min-max games in spaces of measures. <br />
<br />
<br />
<br />
<br />
'''October 24, 2022'''<br />
<br />
[[No seminar.]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022 '''<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures<br />
<br />
Abstract: We will give a gentle introduction of weak KAM theory and then reinterpret Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. We will use one-dimensional irreversible diffusion process on torus to illustrate some essential concepts in the weak KAM theory such as the Peierls barrier, the projected Mather/Aubry/Mane sets. We provide alternative proofs for Freidlin-Wentzell's variational formulas for both self-consistent boundary data at each local attractors and for the rate function are formulated as the global adjustment for the boundary data and the local trimming from the lifted Peierls barriers. Based on this, we proved the rate function is a weak KAM solution to the corresponding stationary Hamilton-Jacobi equation satisfying the selected boundary data on projected Aubry set, which is also the maximal Lipschitz continuous viscosity solution. The rate function is the selected unique weak KAM solution and also serves as the global energy landscape of the original stochastic process. A probability interpretation of the global energy landscape from the weak KAM perspective will also be discussed.<br />
<br />
<br />
<br />
'''November 7, 2022 '''<br />
<br />
[[Beomjun Choi]] (Postech)<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: Liouville theorem for surfaces translating by powers of Gauss curvature<br />
<br />
Abstract: We classify the entire solutions to degenerate Monge-Ampere equations $\det D^2u = (1+|Du|^2)^\beta$ on $\mathbb{R}^2$ for all $\beta<0$. The graphs of such solutions are the translating solitons to the flows by sub-affine-critical powers of Gauss curvature. In view of the Legendre transformation, this classifies the entire solutions to $\det D^2v = (1+|x|^2)^{-\beta}$ as well.<br />
<br />
For the affine-critical-case $\det D^2u =1$, the celebrated result by Jorgens, Calabi and Pogorelov shows every solution must be a convex paraboloid and hence the level sets are homothetic ellipses. In our case, the level sets of given solution converge to a circle or a curve with $k$-fold symmetry for some $k>2$. These curves are closed shrinking curves to the curve shortening flows, classified by B. Andrews in 2003. Then we study the moduli space of solutions for each prescribed asymptotics. This is a joint work with K. Choi and S. Kim.<br />
<br />
<br />
<br />
<br />
'''November 14, 2022 '''<br />
<br />
Adrian Tudorascu (West Virginia University). Host: Misha Feldman, Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: Sticky Particles with Sticky Boundary<br />
<br />
Abstract: We study the pressureless Euler system in an arbitrary closed subset of the real line. The reflective boundary condition renders an ill-posed problem. Instead, we show that the sticky boundary condition is natural and yields a well-posed problem which is treated by means of sticky particles solutions, Lagrangian solutions and an appropriate (and natural) reflection principle.<br />
<br />
<br />
<br />
<br />
<br />
'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: online <br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/94877483456?pwd=cG9Ec1dhb2ErcXhFVW1aN2hCYXRBUT09<br />
Meeting ID: 948 7748 3456<br />
Passcode: 303105<br />
<br />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: Sharp scattering results for the 3d cubic NLS<br />
<br />
Abstract: I will discuss several sharp scattering results for three-dimensional cubic nonlinear Schrödinger equations, including both the free NLS and the NLS with an external potential. After reviewing the proof of scattering below the mass/energy ground state threshold, I will discuss some work on scattering at the threshold for NLS with repulsive potentials. The talk will discuss joint works with B. Dodson; R. Killip, M. Visan, and J. Zheng; and C. Miao and J. Zheng.<br />
<br />
<br />
<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 />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: Solitary waves for infinite depth gravity water waves with constant vorticity<br />
<br />
Abstract: We show that solitary waves exist for pure gravity water waves in infinite depth in the presence of constant (nonzero) vorticity. The proof relies on the fact that this particular water-wave system is well-approximated by the Benjamin-Ono equation, which also allows a description of the profile of the solitary wave in terms of the Benjamin-Ono soliton. This is joint work with Lizhe Wan.<br />
<br />
<br />
<br />
<br />
<br />
'''December 12, 2022 '''<br />
<br />
[[Calum Rickard ]] UC Davis<br />
<br />
Format: in-person in room VV901 <br />
<br />
Time: 3:00 PM -4:00 PM <br />
<br />
Title: An infinite class of shocks for compressible Euler<br />
<br />
Abstract: <br />
We consider the two dimensional compressible Euler equations with azimuthal symmetry and construct an infinite class of shocks by establishing shock formation for a new Hölder family of so-called pre-shocks for all nonnegative integers. Moreover, a precise description of the dominant Riemann variable in the Hölder space is given in the form of a fractional series expansion. This is joint work with Sameer Iyer, Steve Shkoller and Vlad Vicol.<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=24165PDE Geometric Analysis seminar2023-01-09T20:25:02Z<p>Angenent: </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 />
[[No Seminar]]<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 />
Date/time/place: Monday, October 10, 3:30-4:30 pm, VV 901 (if more space will be needed, we have VV B119 to migrate to).<br />
<br />
Speaker: Sasha Kiselev (Duke)<br />
<br />
Title: The flow of polynomial roots under differentiation<br />
Abstract: The question of how polynomial roots move under differentiation is classical. Contributions to this subject have been made by Gauss, Lucas, Marcel Riesz, Polya and many others. In 2018, Stefan Steinerberger derived formally a PDE that should describe the dynamics of roots under differentiation in certain situations. The PDE in question is of hydrodynamic type and bears a striking resemblance to the models used in mathematical biology to describe collective behavior and flocking of various species- such as fish, birds or ants. I will discuss joint work<br />
with Changhui Tan in which we establish global regularity of Steinerberger's equation and make a rigorous connection between its solutions and evolution of roots under differentiation for a class of trigonometric polynomials.<br />
<br />
<br />
<br />
'''October 17, 2022'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
'''Title:''' Analysis of adversarial robustness and of other problems in modern machine learning.<br />
<br />
'''Abstract:''' Modern machine learning methods, in particular deep learning approaches, have enjoyed unparalleled success in a variety of challenging application fields like image recognition, medical image reconstruction, and natural language processing. While a vast majority of previous research in machine learning mainly focused on constructing and understanding models with high predictive power, consensus has emerged that other properties like stability and robustness of models are of equal importance and in many applications essential. This has motivated researchers to investigate the problem of adversarial training (or how to make models robust to adversarial attacks), but despite the development of several computational strategies for adversarial training and some theoretical development in the broader distributionally robust optimization literature, there are still several theoretical questions about it that remain relatively unexplored. In this talk, I will take an analytical perspective on the adversarial robustness problem and explore three questions: 1)What is the connection between adversarial robustness and inverse problems?, 2) Can we use analytical tools to find lower bounds for adversarial robustness problems?, 3) How do we use modern tools from analysis and geometry to solve adversarial robustness problems? At its heart, this talk is an invitation to view adversarial machine learning through the lens of mathematical analysis, showcasing a variety of rich connections with perimeter minimization problems, optimal transport, mean field PDEs of interacting particle systems, and min-max games in spaces of measures. <br />
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'''October 24, 2022'''<br />
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[[No seminar.]]<br />
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Format: , Time: <br />
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'''October 31, 2022 '''<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
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Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures<br />
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Abstract: We will give a gentle introduction of weak KAM theory and then reinterpret Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. We will use one-dimensional irreversible diffusion process on torus to illustrate some essential concepts in the weak KAM theory such as the Peierls barrier, the projected Mather/Aubry/Mane sets. We provide alternative proofs for Freidlin-Wentzell's variational formulas for both self-consistent boundary data at each local attractors and for the rate function are formulated as the global adjustment for the boundary data and the local trimming from the lifted Peierls barriers. Based on this, we proved the rate function is a weak KAM solution to the corresponding stationary Hamilton-Jacobi equation satisfying the selected boundary data on projected Aubry set, which is also the maximal Lipschitz continuous viscosity solution. The rate function is the selected unique weak KAM solution and also serves as the global energy landscape of the original stochastic process. A probability interpretation of the global energy landscape from the weak KAM perspective will also be discussed.<br />
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'''November 7, 2022 '''<br />
<br />
[[Beomjun Choi]] (Postech)<br />
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Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
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Title: Liouville theorem for surfaces translating by powers of Gauss curvature<br />
<br />
Abstract: We classify the entire solutions to degenerate Monge-Ampere equations $\det D^2u = (1+|Du|^2)^\beta$ on $\mathbb{R}^2$ for all $\beta<0$. The graphs of such solutions are the translating solitons to the flows by sub-affine-critical powers of Gauss curvature. In view of the Legendre transformation, this classifies the entire solutions to $\det D^2v = (1+|x|^2)^{-\beta}$ as well.<br />
<br />
For the affine-critical-case $\det D^2u =1$, the celebrated result by Jorgens, Calabi and Pogorelov shows every solution must be a convex paraboloid and hence the level sets are homothetic ellipses. In our case, the level sets of given solution converge to a circle or a curve with $k$-fold symmetry for some $k>2$. These curves are closed shrinking curves to the curve shortening flows, classified by B. Andrews in 2003. Then we study the moduli space of solutions for each prescribed asymptotics. This is a joint work with K. Choi and S. Kim.<br />
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'''November 14, 2022 '''<br />
<br />
Adrian Tudorascu (West Virginia University). Host: Misha Feldman, Hung Tran.<br />
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Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
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Title: Sticky Particles with Sticky Boundary<br />
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Abstract: We study the pressureless Euler system in an arbitrary closed subset of the real line. The reflective boundary condition renders an ill-posed problem. Instead, we show that the sticky boundary condition is natural and yields a well-posed problem which is treated by means of sticky particles solutions, Lagrangian solutions and an appropriate (and natural) reflection principle.<br />
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<br />
'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: online <br />
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Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/94877483456?pwd=cG9Ec1dhb2ErcXhFVW1aN2hCYXRBUT09<br />
Meeting ID: 948 7748 3456<br />
Passcode: 303105<br />
<br />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: Sharp scattering results for the 3d cubic NLS<br />
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Abstract: I will discuss several sharp scattering results for three-dimensional cubic nonlinear Schrödinger equations, including both the free NLS and the NLS with an external potential. After reviewing the proof of scattering below the mass/energy ground state threshold, I will discuss some work on scattering at the threshold for NLS with repulsive potentials. The talk will discuss joint works with B. Dodson; R. Killip, M. Visan, and J. Zheng; and C. Miao and J. Zheng.<br />
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'''November 28, 2022 '''<br />
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[[No Seminar]]- Thanksgiving <br />
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'''December 5, 2022 '''<br />
<br />
[[James Rowan]] (UC Berkeley)<br />
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Time: 3:30 PM -4:30 PM <br />
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Title: Solitary waves for infinite depth gravity water waves with constant vorticity<br />
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Abstract: We show that solitary waves exist for pure gravity water waves in infinite depth in the presence of constant (nonzero) vorticity. The proof relies on the fact that this particular water-wave system is well-approximated by the Benjamin-Ono equation, which also allows a description of the profile of the solitary wave in terms of the Benjamin-Ono soliton. This is joint work with Lizhe Wan.<br />
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'''December 12, 2022 '''<br />
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[[Calum Rickard ]] UC Davis<br />
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Format: in-person in room VV901 <br />
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Time: 3:00 PM -4:00 PM <br />
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Title: An infinite class of shocks for compressible Euler<br />
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Abstract: <br />
We consider the two dimensional compressible Euler equations with azimuthal symmetry and construct an infinite class of shocks by establishing shock formation for a new Hölder family of so-called pre-shocks for all nonnegative integers. Moreover, a precise description of the dominant Riemann variable in the Hölder space is given in the form of a fractional series expansion. This is joint work with Sameer Iyer, Steve Shkoller and Vlad Vicol.<br />
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'''January 30, 2023 '''<br />
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[[James Rowan|Jingwen Chen]] (U Chicago)<br />
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Time: 3:30 PM -4:30 PM, in person in VV901 <br />
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Title: Mean curvature flows in the sphere via phase transitions.<br />
<br />
Abstract: In this talk, we will discuss some solutions of the mean curvature flow (MCF) of surfaces in the 3-sphere. We will recall a generalized notion of MCF introduced by Brakke in the 70s, as well as its regularization by a parabolic partial differential equation arising in the theory of phase transitions. We will talk about some existence problems for this parabolic equation, and use them to construct MCFs that join minimal surfaces of low area in the 3-sphere, and some recent progress on the spaces of MCFs using Morse-Bott theory. <br />
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This is joint work with Pedro Gaspar (Pontificia Universidad Católica de Chile). <br />
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'''March 27, 2023'''<br />
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[[Yuan Gao|Matt Jacobs]] (Purdue). Host: Hung Tran.<br />
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'''April 17, 2023'''<br />
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[[Jingrui Cheng]] (Stony Brook). Host: Misha Feldman.<br />
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Format: , Time: <br />
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Title:<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 />
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'''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 />
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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 />
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<br />
'''February 14th, 2022.'''<br />
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[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:910, Time:3:30PM <br />
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Title: MCF after the Velázquez&mdash;Stolarski example.<br />
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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 />
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'''February 21th, 2022.'''<br />
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[[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 />
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'''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 />
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<br />
'''March 21th, 2022.'''<br />
<br />
[[ No Seminar]];<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 />
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<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 />
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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 />
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<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 />
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<br />
'''April 25th, 2022.'''<br />
<br />
[[No seminar]]<br />
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'''May 2nd, 2022.'''<br />
<br />
[[Alexei Gazca]]; Format: online seminar via Zoom, Time:3:30PM -4:30PM<br />
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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 />
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<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 />
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<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=24163PDE Geometric Analysis seminar2023-01-09T15:58:09Z<p>Angenent: added announcement for Jingwen Chen's talk on Jan 30</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 />
[[No Seminar]]<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 />
Date/time/place: Monday, October 10, 3:30-4:30 pm, VV 901 (if more space will be needed, we have VV B119 to migrate to).<br />
<br />
Speaker: Sasha Kiselev (Duke)<br />
<br />
Title: The flow of polynomial roots under differentiation<br />
Abstract: The question of how polynomial roots move under differentiation is classical. Contributions to this subject have been made by Gauss, Lucas, Marcel Riesz, Polya and many others. In 2018, Stefan Steinerberger derived formally a PDE that should describe the dynamics of roots under differentiation in certain situations. The PDE in question is of hydrodynamic type and bears a striking resemblance to the models used in mathematical biology to describe collective behavior and flocking of various species- such as fish, birds or ants. I will discuss joint work<br />
with Changhui Tan in which we establish global regularity of Steinerberger's equation and make a rigorous connection between its solutions and evolution of roots under differentiation for a class of trigonometric polynomials.<br />
<br />
<br />
<br />
'''October 17, 2022'''<br />
<br />
[[Nicolas Garca Trillos]] (Stats, UW Madison). Host: Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
'''Title:''' Analysis of adversarial robustness and of other problems in modern machine learning.<br />
<br />
'''Abstract:''' Modern machine learning methods, in particular deep learning approaches, have enjoyed unparalleled success in a variety of challenging application fields like image recognition, medical image reconstruction, and natural language processing. While a vast majority of previous research in machine learning mainly focused on constructing and understanding models with high predictive power, consensus has emerged that other properties like stability and robustness of models are of equal importance and in many applications essential. This has motivated researchers to investigate the problem of adversarial training (or how to make models robust to adversarial attacks), but despite the development of several computational strategies for adversarial training and some theoretical development in the broader distributionally robust optimization literature, there are still several theoretical questions about it that remain relatively unexplored. In this talk, I will take an analytical perspective on the adversarial robustness problem and explore three questions: 1)What is the connection between adversarial robustness and inverse problems?, 2) Can we use analytical tools to find lower bounds for adversarial robustness problems?, 3) How do we use modern tools from analysis and geometry to solve adversarial robustness problems? At its heart, this talk is an invitation to view adversarial machine learning through the lens of mathematical analysis, showcasing a variety of rich connections with perimeter minimization problems, optimal transport, mean field PDEs of interacting particle systems, and min-max games in spaces of measures. <br />
<br />
<br />
<br />
<br />
'''October 24, 2022'''<br />
<br />
[[No seminar.]]<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''October 31, 2022 '''<br />
<br />
[[Yuan Gao]] (Purdue). Host: Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures<br />
<br />
Abstract: We will give a gentle introduction of weak KAM theory and then reinterpret Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. We will use one-dimensional irreversible diffusion process on torus to illustrate some essential concepts in the weak KAM theory such as the Peierls barrier, the projected Mather/Aubry/Mane sets. We provide alternative proofs for Freidlin-Wentzell's variational formulas for both self-consistent boundary data at each local attractors and for the rate function are formulated as the global adjustment for the boundary data and the local trimming from the lifted Peierls barriers. Based on this, we proved the rate function is a weak KAM solution to the corresponding stationary Hamilton-Jacobi equation satisfying the selected boundary data on projected Aubry set, which is also the maximal Lipschitz continuous viscosity solution. The rate function is the selected unique weak KAM solution and also serves as the global energy landscape of the original stochastic process. A probability interpretation of the global energy landscape from the weak KAM perspective will also be discussed.<br />
<br />
<br />
<br />
'''November 7, 2022 '''<br />
<br />
[[Beomjun Choi]] (Postech)<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: Liouville theorem for surfaces translating by powers of Gauss curvature<br />
<br />
Abstract: We classify the entire solutions to degenerate Monge-Ampere equations $\det D^2u = (1+|Du|^2)^\beta$ on $\mathbb{R}^2$ for all $\beta<0$. The graphs of such solutions are the translating solitons to the flows by sub-affine-critical powers of Gauss curvature. In view of the Legendre transformation, this classifies the entire solutions to $\det D^2v = (1+|x|^2)^{-\beta}$ as well.<br />
<br />
For the affine-critical-case $\det D^2u =1$, the celebrated result by Jorgens, Calabi and Pogorelov shows every solution must be a convex paraboloid and hence the level sets are homothetic ellipses. In our case, the level sets of given solution converge to a circle or a curve with $k$-fold symmetry for some $k>2$. These curves are closed shrinking curves to the curve shortening flows, classified by B. Andrews in 2003. Then we study the moduli space of solutions for each prescribed asymptotics. This is a joint work with K. Choi and S. Kim.<br />
<br />
<br />
<br />
<br />
'''November 14, 2022 '''<br />
<br />
Adrian Tudorascu (West Virginia University). Host: Misha Feldman, Hung Tran.<br />
<br />
Format: in person, Time: 3:30pm-4:30pm VV 901 <br />
<br />
Title: Sticky Particles with Sticky Boundary<br />
<br />
Abstract: We study the pressureless Euler system in an arbitrary closed subset of the real line. The reflective boundary condition renders an ill-posed problem. Instead, we show that the sticky boundary condition is natural and yields a well-posed problem which is treated by means of sticky particles solutions, Lagrangian solutions and an appropriate (and natural) reflection principle.<br />
<br />
<br />
<br />
<br />
<br />
'''November 21, 2022 '''<br />
<br />
[[Jason Murphy]] (Missouri S&T)<br />
<br />
Format: online <br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/94877483456?pwd=cG9Ec1dhb2ErcXhFVW1aN2hCYXRBUT09<br />
Meeting ID: 948 7748 3456<br />
Passcode: 303105<br />
<br />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: Sharp scattering results for the 3d cubic NLS<br />
<br />
Abstract: I will discuss several sharp scattering results for three-dimensional cubic nonlinear Schrödinger equations, including both the free NLS and the NLS with an external potential. After reviewing the proof of scattering below the mass/energy ground state threshold, I will discuss some work on scattering at the threshold for NLS with repulsive potentials. The talk will discuss joint works with B. Dodson; R. Killip, M. Visan, and J. Zheng; and C. Miao and J. Zheng.<br />
<br />
<br />
<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 />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: Solitary waves for infinite depth gravity water waves with constant vorticity<br />
<br />
Abstract: We show that solitary waves exist for pure gravity water waves in infinite depth in the presence of constant (nonzero) vorticity. The proof relies on the fact that this particular water-wave system is well-approximated by the Benjamin-Ono equation, which also allows a description of the profile of the solitary wave in terms of the Benjamin-Ono soliton. This is joint work with Lizhe Wan.<br />
<br />
<br />
<br />
<br />
<br />
'''December 12, 2022 '''<br />
<br />
[[Calum Rickard ]] UC Davis<br />
<br />
Format: in-person in room VV901 <br />
<br />
Time: 3:00 PM -4:00 PM <br />
<br />
Title: An infinite class of shocks for compressible Euler<br />
<br />
Abstract: <br />
We consider the two dimensional compressible Euler equations with azimuthal symmetry and construct an infinite class of shocks by establishing shock formation for a new Hölder family of so-called pre-shocks for all nonnegative integers. Moreover, a precise description of the dominant Riemann variable in the Hölder space is given in the form of a fractional series expansion. This is joint work with Sameer Iyer, Steve Shkoller and Vlad Vicol.<br />
<br />
<br />
<br />
'''January 30, 2023 '''<br />
<br />
[[James Rowan|Jingwen Chen]] (U Chicago)<br />
<br />
Time: 3:30 PM -4:30 PM <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''March 27, 2023'''<br />
<br />
[[Yuan Gao|Matt Jacobs]] (Purdue). Host: Hung Tran.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<br />
<br />
<br />
<br />
<br />
<br />
'''April 17, 2023'''<br />
<br />
[[Jingrui Cheng]] (Stony Brook). Host: Misha Feldman.<br />
<br />
Format: , Time: <br />
<br />
Title:<br />
<br />
Abstract:<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23645PDE Geometric Analysis seminar2022-09-13T21:01:45Z<p>Angenent: /* PDE GA Seminar Schedule Fall 2022-Spring 2023 */</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 />
<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23644PDE Geometric Analysis seminar2022-09-13T20:59:14Z<p>Angenent: </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: 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 />
'''Title:''' ''Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up''<br />
<br />
Abstract: 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 />
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Title:<br />
<br />
Abstract:<br />
<br />
<br />
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<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23643PDE Geometric Analysis seminar2022-09-13T20:57:23Z<p>Angenent: </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: 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 />
Title: Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up<br />
<br />
Abstract: 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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23637PDE Geometric Analysis seminar2022-09-12T19:30:25Z<p>Angenent: </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: 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 />
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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=23636PDE Geometric Analysis seminar2022-09-12T19:02:21Z<p>Angenent: </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: 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 />
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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=22520PDE Geometric Analysis seminar2022-01-22T17:19:20Z<p>Angenent: /* Spring 2022 */</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 />
<br />
For now we would like to provide a zoom link where one is required to register. This way you will receive weekly reminders/info about the upcoming talks.<br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP <br />
<br />
After registering, you will receive a confirmation email containing information about joining the meeting. <br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
=Spring 2022=<br />
<br />
<br />
'''January 31th, 2022.'''<br />
<br />
[[TBA]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''February 7th, 2022.'''<br />
<br />
[[TBA]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''February 14th, 2022.'''<br />
<br />
[[Sigurd Angenent]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <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, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''February 28th, 2021.'''<br />
<br />
[[Michael Hott]]; Format: online seminar via Zoom, Time:3:30PM-4:30PM<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''March 7th, 2022.'''<br />
<br />
[[TBA]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''March 14th, 2022.'''<br />
<br />
[[Spring recess - No Seminar]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''March 21th, 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 />
'''March 28th, 2022.'''<br />
<br />
[[Monica Visan]]; Format: online seminar via Zoom, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''April 4th, 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 />
'''April 11th, 2022.'''<br />
<br />
[[Dallas Albitron]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<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]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''May 1th, 2022.'''<br />
<br />
[[TBA]]; Format: online seminar via Zoom/ in person, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=21987PDE Geometric Analysis seminar2021-10-22T21:35:18Z<p>Angenent: </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 />
<br />
For now we would like to provide a zoom link where one is required to register. This way you will receive weekly reminders/info about the upcoming talks.<br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP <br />
<br />
After registering, you will receive a confirmation email containing information about joining the meeting. <br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
<br />
<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 />
<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 />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, Room:--, Time:-- <br />
<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
TBA<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
No seminar <br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
TBA<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
TBA<br />
<br />
<br />
'''February 21th, 2021.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=21825PDE Geometric Analysis seminar2021-10-01T19:38:06Z<p>Angenent: </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 />
<br />
For now we would like to provide a zoom link where one is required to register. This way you will receive weekly reminders/info about the upcoming talks.<br />
<br />
Register in advance for this meeting: https://uwmadison.zoom.us/meeting/register/tJcpcuqqqjMjE9VJ_-SaJ0gc6kS10CCTQTVP <br />
<br />
After registering, you will receive a confirmation email containing information about joining the meeting. <br />
<br />
== PDE GA Seminar Schedule Fall 2021-Spring 2022 ==<br />
<br />
<br />
<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 />
TBA<br />
<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: TBA<br />
<br />
Abstract: TBA<br />
<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: TBA<br />
<br />
Abstract:<br />
<br />
<br />
'''November 1th, 2021.'''<br />
<br />
[[ Albert Ai]] (UW Madison); <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''November 8th, 2021.'''<br />
<br />
[[Lizhe Wan]] (UW Madison); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''November 15th, 2021.'''<br />
<br />
[[Sebastien Herr]] (Bielefeld University); Format: online seminar via Zoom, Room:--, Time:-- <br />
<br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
<br />
'''November 22th, 2021.'''<br />
<br />
TBA<br />
<br />
<br />
'''November 29th, 2021.'''<br />
<br />
No seminar <br />
<br />
<br />
'''December 6th, 2021.'''<br />
<br />
TBA<br />
<br />
<br />
'''December 13th, 2021.'''<br />
<br />
TBA<br />
<br />
<br />
'''February 21th, 2021.'''<br />
<br />
[[Birgit Schoerkhuber]]; Format: online seminar via Zoom, Room:--, Time:-- <br />
<br />
Title: TBA<br />
<br />
Abstract: TBA<br />
<br />
<br />
'''April 25th, 2022.'''<br />
<br />
[[Loc Nguyen]] (UNCC); Format: in-person seminar, Room: 901, Time: 3:30PM-4:30PM. Host: Hung Tran.<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>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=19157PDE Geometric Analysis seminar2020-02-26T16:12:02Z<p>Angenent: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<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 />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]<br />
| Kim and Tran<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Mathew Langford | Concavity of the arrival time ]]<br />
| Angenent<br />
|- <br />
|Dec 9 - Colloquium (4-5PM)<br />
| Hui Yu (Columbia)<br />
|[[#Hui Yu | TBA ]]<br />
| Tran<br />
|- <br />
|Feb. 3<br />
| Philippe LeFloch (Sorbonne University and CNRS)<br />
|[[#Philippe LeFloch | Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions ]]<br />
| Feldman<br />
|- <br />
|Feb. 10<br />
| Joonhyun La (Stanford)<br />
|[[#Joonhyun La | On a kinetic model of polymeric fluids ]]<br />
| Kim<br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]<br />
| Tran<br />
|- <br />
|Feb 19 - Colloquium (4-5PM)<br />
| Zhenfu Wang (University of Pennsylvania)<br />
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | Polygonal Pancakes ]]<br />
| Angenent<br />
|- <br />
|March 3 -- Analysis seminar<br />
| William Green (Rose-Hulman Institute of Technology)<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy Stovall<br />
|-<br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| Schrecker<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|April 6<br />
| Zhiyan Ding (UW Madison)<br />
|[[#Zhiyan Ding | Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis ]]<br />
| Kim and Tran<br />
|- <br />
|April 13<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 20<br />
| Adrian Tudorascu (WVU)<br />
|[[#Adrian Tudorascu | On the Lagrangian description of the Sticky Particle flow ]]<br />
| Feldman<br />
|- <br />
|April 27<br />
| Christof Sparber (UIC)<br />
|[[#Christof Sparber | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.<br />
<br />
===Ilyas Khan===<br />
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.<br />
<br />
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.<br />
<br />
===Mathew Langford===<br />
Title: Concavity of the arrival time<br />
<br />
Abstract: We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a novel concavity maximum principle argument to the corresponding level set flow equations. In particular, this yields a short proof of Hamilton’s differential Harnack inequality for mean curvature flow and, more generally, Andrews’ differential Harnack inequalities for certain “$\alpha$-inverse-concave” flows.<br />
<br />
===Philippe LeFloch===<br />
Title: Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions<br />
<br />
Abstract: I will present recent progress on the global evolution problem for self-gravitating matter. (1) For Einstein's constraint equations, motivated by a scheme proposed by Carlotto and Schoen I will show the existence of asymptotically Euclidean Einstein spaces with low decay; joint work with T. Nguyen. <br />
<br />
(2) For Einstein's evolution equations in the regime near Minkowski spacetime, I will show the global nonlinear stability of massive matter fields; joint work with Y. Ma. <br />
<br />
(3) For the colliding gravitational wave problem, I will show the existence of weakly regular spacetimes containing geometric singularities across which junction conditions are imposed; joint work with B. Le Floch and G. Veneziano.<br />
<br />
<br />
===Joonhyun La===<br />
Title: On a kinetic model of polymeric fluids<br />
<br />
Abstract: In this talk, we prove global well-posedness of a system describing behavior of dilute flexible polymeric fluids. This model is based on kinetic theory, and a main difficulty for this system is its multi-scale nature. A new function space, based on moments, is introduced to address this issue, and this function space allows us to deal with larger initial data.<br />
<br />
<br />
===Yannick Sire===<br />
Title: Minimizers for the thin one-phase free boundary problem<br />
<br />
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe. <br />
<br />
===Matthew Schrecker===<br />
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations<br />
<br />
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.<br />
<br />
===Theodora Bourni===<br />
Title: Polygonal Pancakes<br />
<br />
Abstract: We study ancient collapsed solutions to mean curvature flow, $\{M^n_t\}_{t\in(-\infty,0)}$, in terms of their squash down: $\Omega_*=\lim_{t\to-\infty}\frac{1}{-t} M_t$. We show that $\Omega_*$ must be a convex body which circumscribes $S^1$ and for every such $\Omega_*$ we construct a solution with this prescribed squash down. Our analysis includes non-compact examples, in which setting we disprove a conjecture of White stating that all eternal solutions must be translators. This is joint work with Langford and Tinaglia.<br />
<br />
===Zhiyan Ding===<br />
Title: Ensemble Kalman Sampling: well-posedness, mean-field limit and convergence analysis<br />
<br />
Abstract: Ensemble Kalman Sampling (EKS) is a method to find iid samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. In this talk, I will focus on the continuous version of EKS with linear forward map, a coupled SDE system. I will talk about its well-posedness and justify its mean-filed limit is a Fokker-Planck equation, whose equilibrium state is the target distribution.<br />
<br />
===Adrian Tudorascu===<br />
Title: On the Lagrangian description of the Sticky Particle flow <br />
<br />
Abstract: R. Hynd has recently proved that for absolutely continuous initial velocities the Sticky Particle system admits solutions described by monotone flow maps in Lagrangian coordinates. We present a generalization of this result to general initial velocities and discuss some consequences. (This is based on ongoing work with M. Suder.)</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=18473PDE Geometric Analysis seminar2019-11-22T22:39:18Z<p>Angenent: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<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 />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| <br />
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html ]]<br />
| <br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 28-29, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=993<br />
| | Recent progress in analytical aspects of kinetic equations and related fluid models <br />
| <br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 25-27, VV901<br />
| https://www.ki-net.umd.edu/content/conf?event_id=1015<br />
|| Forward and Inverse Problems in Kinetic Theory <br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]<br />
| Kim and Tran<br />
|- <br />
|Nov 18<br />
| Ilyas Khan (UW Madison)<br />
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]<br />
| Kim and Tran<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Mathew Langford | Concavity of the arrival time ]]<br />
| Angenent<br />
|- <br />
|Dec 9 - Colloquium (4-5PM)<br />
| Hui Yu (Columbia)<br />
|[[#Hui Yu | TBA ]]<br />
| Tran<br />
|- <br />
|Feb. 3<br />
| Philippe LeFloch (Sorbonne Université)<br />
|[[#Speaker | TBA ]]<br />
| Feldman<br />
|- <br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Matthew Schrecker (UW Madison)<br />
|[[#Matthew Schrecker | TBA ]]<br />
| Feldman<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Ian Tice (CMU)<br />
|[[#Ian Tice| TBA ]]<br />
| Kim<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Huy Nguyen (Brown)<br />
|[[#Huy Nguyen | TBA ]]<br />
| organizer<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 20<br />
| Hyunju Kwon (IAS)<br />
|[[#Hyunju Kwon | TBA ]]<br />
| Kim<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|May 18-21<br />
| Madison Workshop in PDE 2020<br />
|[[#Speaker | TBA ]]<br />
| Tran<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Scott Smith===<br />
<br />
Title: Recent progress on singular, quasi-linear stochastic PDE<br />
<br />
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory. They require flexibility in the notion of solution as well as new a priori bounds. Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.<br />
<br />
<br />
===Son Tu===<br />
<br />
Title: State-Constraint static Hamilton-Jacobi equations in nested domains<br />
<br />
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases, the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).<br />
<br />
<br />
===Jin Woo Jang===<br />
<br />
Title: On a Cauchy problem for the Landau-Boltzmann equation<br />
<br />
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.<br />
<br />
<br />
===Stefania Patrizi===<br />
<br />
Title: <br />
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity<br />
<br />
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic limit of solutions of Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is joint work with E. Valdinoci.<br />
<br />
<br />
===Claude Bardos===<br />
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture<br />
<br />
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.<br />
<br />
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.<br />
<br />
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.<br />
<br />
===Albert Ai===<br />
Title: Two dimensional gravity waves at low regularity: Energy estimates<br />
<br />
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.<br />
<br />
===Ilyas Khan===<br />
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.<br />
<br />
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.<br />
<br />
===Mathew Langford===<br />
Title: Concavity of the arrival time<br />
<br />
Abstract: We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a novel concavity maximum principle argument to the corresponding level set flow equations. In particular, this yields a short proof of Hamilton’s differential Harnack inequality for mean curvature flow and, more generally, Andrews’ differential Harnack inequalities for certain “$\alpha$-inverse-concave” flows.</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=17684PDE Geometric Analysis seminar2019-08-27T20:22:20Z<p>Angenent: /* PDE GA Seminar Schedule Fall 2019-Spring 2020 */</p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<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 />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html<br />
|[[ # | ]]<br />
| <br />
|- <br />
|Sep 16<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 30<br />
| Michael Loss (Georgia tech)<br />
|[[#Michael Loss | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Nov 11<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|Nov 18<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|-<br />
|Nov 25<br />
| Mathew Langford (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 20<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=17681PDE Geometric Analysis seminar2019-08-26T18:08:02Z<p>Angenent: /* PDE GA Seminar Schedule Fall 2019-Spring 2020 */</p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==<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 />
|Sep 9<br />
| Scott Smith (UW Madison)<br />
|[[#Scott Smith | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 14-15<br />
| AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html<br />
|[[ # | ]]<br />
| <br />
|- <br />
|Sep 16<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|Sep 23<br />
| Son Tu (UW Madison)<br />
|[[#Son Tu | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Sep 30<br />
| Michael Loss (Georgia tech)<br />
|[[#Michael Loss | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 7<br />
| Jin Woo Jang (Postech)<br />
|[[#Speaker | TBA ]]<br />
| Kim<br />
|- <br />
|Oct 14<br />
| Stefania Patrizi (UT Austin)<br />
|[[#Stefania Patrizi | TBA ]]<br />
| Tran<br />
|- <br />
|Oct 21<br />
| Claude Bardos (Université Paris Denis Diderot, France)<br />
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]<br />
| Li<br />
|- <br />
|Oct 28<br />
| Albert Ai (UW Madison)<br />
|[[#Albert Ai | TBA ]]<br />
| Ifrim<br />
|- <br />
|Nov 4<br />
| Yunbai Cao (UW Madison)<br />
|[[#Yunbai Cao | TBA ]]<br />
| Kim and Tran<br />
|- <br />
|Nov 11<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|- <br />
|- <br />
|- <br />
|Feb 17<br />
| Yannick Sire (JHU)<br />
|[[#Yannick Sire (JHU) | TBA ]]<br />
| Tran<br />
|- <br />
|Feb 24<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 2<br />
| Theodora Bourni (UT Knoxville)<br />
|[[#Speaker | TBA ]]<br />
| Angenent<br />
|- <br />
|March 9<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 16 <br />
| No seminar (spring break)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|March 23<br />
| Jared Speck (Vanderbilt)<br />
|[[#Jared Speck | TBA ]]<br />
| SCHRECKER<br />
|- <br />
|March 30<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 6<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 13<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 20<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|- <br />
|April 27<br />
| Speaker (Institute)<br />
|[[#Speaker | TBA ]]<br />
| Host<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== ===<br />
<br />
Title: <br />
<br />
Abstract:</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17680Colloquia/Spring20202019-08-26T17:05:17Z<p>Angenent: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Shamgar Gurevitch (Madison)<br />
|<br />
|-<br />
|Oct 18<br />
| Thomas Strohmer (UC Davis)<br />
|<br />
|Gurevich<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=16648PDE Geometric Analysis seminar2019-01-18T11:19:25Z<p>Angenent: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==<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 />
|August 31 (FRIDAY),<br />
| Julian Lopez-Gomez (Complutense University of Madrid)<br />
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]<br />
| Rabinowitz<br />
<br />
|- <br />
|September 10,<br />
| Hiroyoshi Mitake (University of Tokyo)<br />
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]<br />
| Tran<br />
|- <br />
|September 12 and September 14,<br />
| Gunther Uhlmann (UWash)<br />
|[[#Gunther Uhlmann | TBA ]]<br />
| Li<br />
|- <br />
|September 17,<br />
| Changyou Wang (Purdue)<br />
|[[#Changyou Wang | Some recent results on mathematical analysis of Ericksen-Leslie System ]]<br />
| Tran<br />
|-<br />
|Sep 28, Colloquium<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|- <br />
|October 1,<br />
| Matthew Schrecker (UW)<br />
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]<br />
| Kim and Tran<br />
|- <br />
|October 8,<br />
| Anna Mazzucato (PSU)<br />
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]<br />
| Li and Kim<br />
|- <br />
|October 15,<br />
| Lei Wu (Lehigh)<br />
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]<br />
| Kim<br />
|- <br />
|October 22,<br />
| Annalaura Stingo (UCD)<br />
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]<br />
| Mihaela Ifrim<br />
|- <br />
|October 29,<br />
| Yeon-Eung Kim (UW)<br />
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]<br />
| Kim and Tran<br />
|- <br />
|November 5,<br />
| Albert Ai (UC Berkeley)<br />
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]<br />
| Mihaela Ifrim<br />
|- <br />
|Nov 7 (Wednesday), Colloquium<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|-<br />
|December 3, ''' Time: 3:00, Room: B223 Van Vleck '''<br />
| Trevor Leslie (UW)<br />
|[[#Trevor Leslie | Flocking Models with Singular Interaction Kernels ]]<br />
| Kim and Tran <br />
|-<br />
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''<br />
|Serena Federico (MIT)<br />
|[[#Serena Federico | Sufficient conditions for local solvability of some degenerate partial differential operators ]]<br />
| Mihaela Ifrim <br />
|- <br />
|December 10, Colloquium, '''Time: 4:00''' <br />
| [https://math.mit.edu/~maxe/ Max Engelstein] (MIT)<br />
|[[# Max Engelstein| The role of Energy in Regularity ]]<br />
| Feldman<br />
|- <br />
|January 28,<br />
| Ru-Yu Lai (Minnesota)<br />
|[[# Ru-Yu Lai | TBA ]]<br />
| Li and Kim <br />
|-<br />
|January 29, '''4:00 p.m. in VV B139'''<br />
| Trevor Leslie (UW-Madison)<br />
|[[# Trevor Leslie| TBA ]]<br />
| Analysis seminar<br />
|-<br />
| February 4,<br />
|<br />
|[[# | No seminar (several relevant colloquiums in Jan/30-Feb/8)]]<br />
| <br />
|-<br />
| February 11,<br />
| Seokbae Yun (SKKU, long term visitor of UW-Madison)<br />
|[[# Seokbae Yun | TBA ]]<br />
| Kim <br />
|- <br />
| February 18, '''Room: VV B239'''<br />
| Daniel Tataru (Berkeley)<br />
|[[# Daniel Tataru | TBA ]]<br />
| Ifrim <br />
|- <br />
| February 19,<br />
| Wenjia Jing (Tsinghua University)<br />
|[[#Wenjia Jing | TBA ]]<br />
| Tran<br />
|- <br />
|February 25,<br />
| Xiaoqin Guo (UW)<br />
|[[#Xiaoqin Guo | TBA ]]<br />
| Kim and Tran<br />
|-<br />
|March 4 <br />
| Vladimir Sverak (Minnesota)<br />
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]<br />
| Kim<br />
|- <br />
|March 11 <br />
| Jonathan Luk (Stanford)<br />
|[[#Jonathan Luk | TBA ]]<br />
| Kim<br />
|-<br />
|March 18,<br />
| Spring recess (Mar 16-24, 2019)<br />
|[[# | ]]<br />
| <br />
|- <br />
|April 1 <br />
| Zaher Hani (Michigan)<br />
|[[#Zaher Hani | TBA ]]<br />
| Ifrim<br />
|-<br />
|April 15,<br />
| Yao Yao (Gatech)<br />
|[[#Yao Yao | TBA ]]<br />
| Tran<br />
|- <br />
|April 22,<br />
| Jessica Lin (McGill University)<br />
|[[#Jessica Lin | TBA ]]<br />
| Tran<br />
|- <br />
|April 29,<br />
| Beomjun Choi (Columbia)<br />
|[[#Beomjun Choi | Evolution of non-compact hypersurfaces by inverse mean curvature]]<br />
| Angenent<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Julian Lopez-Gomez===<br />
<br />
Title: The theorem of characterization of the Strong Maximum Principle<br />
<br />
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.<br />
<br />
===Hiroyoshi Mitake===<br />
Title: On approximation of time-fractional fully nonlinear equations<br />
<br />
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.) <br />
<br />
<br />
<br />
===Changyou Wang===<br />
<br />
Title: Some recent results on mathematical analysis of Ericksen-Leslie System<br />
<br />
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.<br />
<br />
===Matthew Schrecker===<br />
<br />
Title: Finite energy methods for the 1D isentropic Euler equations<br />
<br />
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.<br />
<br />
===Anna Mazzucato===<br />
<br />
Title: On the vanishing viscosity limit in incompressible flows<br />
<br />
Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.<br />
<br />
===Lei Wu===<br />
<br />
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects<br />
<br />
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.<br />
<br />
<br />
===Annalaura Stingo===<br />
<br />
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D<br />
<br />
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms » .<br />
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.<br />
<br />
===Yeon-Eung Kim===<br />
<br />
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties<br />
<br />
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.<br />
<br />
===Albert Ai===<br />
<br />
Title: Low Regularity Solutions for Gravity Water Waves<br />
<br />
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.<br />
<br />
===Trevor Leslie===<br />
<br />
Title: Flocking Models with Singular Interaction Kernels<br />
<br />
Abstract: Many biological systems exhibit the property of self-organization, the defining feature of which is coherent, large-scale motion arising from underlying short-range interactions between the agents that make up the system. In this talk, we give an overview of some simple models that have been used to describe the so-called flocking phenomenon. Within the family of models that we consider (of which the Cucker-Smale model is the canonical example), writing down the relevant set of equations amounts to choosing a kernel that governs the interaction between agents. We focus on the recent line of research that treats the case where the interaction kernel is singular. In particular, we discuss some new results on the wellposedness and long-time dynamics of the Euler Alignment model and the Shvydkoy-Tadmor model.<br />
<br />
===Serena Federico===<br />
<br />
Title: Sufficient conditions for local solvability of some degenerate partial differential operators <br />
<br />
Abstract: In this talk we will give sufficient conditions for the local solvability of a class of degenerate second order linear partial differential operators with smooth coefficients. The class under consideration, inspired by some generalizations of the Kannai operator, is characterized by the presence of a complex subprincipal symbol. By giving suitable conditions on the subprincipal part and using the technique of a priori estimates, we will show that the operators in the class are at least $L^2$ to $L^2$ locally solvable.<br />
<br />
===Max Engelstein===<br />
<br />
Title: The role of Energy in Regularity<br />
<br />
Abstract: The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy.<br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field.<br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur.<br />
<br />
===Beomjun Choi===<br />
In this talk, we first introduce the inverse mean curvature flow and its well known application in the the proof of Riemannian Penrose inequality by Huisken and Ilmanen. Then our main result on the existence and behavior of convex non-compact solution will be discussed. <br />
<br />
The key ingredient is a priori interior in time estimate on the inverse mean curvature in terms of the aperture of supporting cone at infinity. This is a joint work with P. Daskalopoulos and I will also mention the recent work with P.-K. Hung concerning the evolution of singular hypersurfaces.</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=16633PDE Geometric Analysis seminar2019-01-16T15:47:09Z<p>Angenent: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===<br />
<br />
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==<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 />
|August 31 (FRIDAY),<br />
| Julian Lopez-Gomez (Complutense University of Madrid)<br />
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]<br />
| Rabinowitz<br />
<br />
|- <br />
|September 10,<br />
| Hiroyoshi Mitake (University of Tokyo)<br />
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]<br />
| Tran<br />
|- <br />
|September 12 and September 14,<br />
| Gunther Uhlmann (UWash)<br />
|[[#Gunther Uhlmann | TBA ]]<br />
| Li<br />
|- <br />
|September 17,<br />
| Changyou Wang (Purdue)<br />
|[[#Changyou Wang | Some recent results on mathematical analysis of Ericksen-Leslie System ]]<br />
| Tran<br />
|-<br />
|Sep 28, Colloquium<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|- <br />
|October 1,<br />
| Matthew Schrecker (UW)<br />
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]<br />
| Kim and Tran<br />
|- <br />
|October 8,<br />
| Anna Mazzucato (PSU)<br />
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]<br />
| Li and Kim<br />
|- <br />
|October 15,<br />
| Lei Wu (Lehigh)<br />
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]<br />
| Kim<br />
|- <br />
|October 22,<br />
| Annalaura Stingo (UCD)<br />
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]<br />
| Mihaela Ifrim<br />
|- <br />
|October 29,<br />
| Yeon-Eung Kim (UW)<br />
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]<br />
| Kim and Tran<br />
|- <br />
|November 5,<br />
| Albert Ai (UC Berkeley)<br />
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]<br />
| Mihaela Ifrim<br />
|- <br />
|Nov 7 (Wednesday), Colloquium<br />
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)<br />
|[[#Nov 7: Luca Spolaor (MIT) | (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]<br />
| Feldman<br />
|-<br />
|December 3, ''' Time: 3:00, Room: B223 Van Vleck '''<br />
| Trevor Leslie (UW)<br />
|[[#Trevor Leslie | Flocking Models with Singular Interaction Kernels ]]<br />
| Kim and Tran <br />
|-<br />
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''<br />
|Serena Federico (MIT)<br />
|[[#Serena Federico | Sufficient conditions for local solvability of some degenerate partial differential operators ]]<br />
| Mihaela Ifrim <br />
|- <br />
|December 10, Colloquium, '''Time: 4:00''' <br />
| [https://math.mit.edu/~maxe/ Max Engelstein] (MIT)<br />
|[[# Max Engelstein| The role of Energy in Regularity ]]<br />
| Feldman<br />
|- <br />
|January 28,<br />
| Ru-Yu Lai (Minnesota)<br />
|[[# Ru-Yu Lai | TBA ]]<br />
| Li and Kim <br />
|-<br />
| February 4,<br />
|<br />
|[[# | No seminar (several relevant colloquiums in Jan/30-Feb/8)]]<br />
| <br />
|-<br />
| February 11,<br />
| Seokbae Yun (SKKU, long term visitor of UW-Madison)<br />
|[[# Seokbae Yun | TBA ]]<br />
| Kim <br />
|- <br />
| February 18, '''Room: VV B239'''<br />
| Daniel Tataru (Berkeley)<br />
|[[# Daniel Tataru | TBA ]]<br />
| Ifrim <br />
|- <br />
| February 19,<br />
| Wenjia Jing (Tsinghua University)<br />
|[[#Wenjia Jing | TBA ]]<br />
| Tran<br />
|- <br />
|February 25,<br />
| Xiaoqin Guo (UW)<br />
|[[#Xiaoqin Guo | TBA ]]<br />
| Kim and Tran<br />
|-<br />
|March 4 <br />
| Vladimir Sverak (Minnesota)<br />
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]<br />
| Kim<br />
|- <br />
|March 11 <br />
| Jonathan Luk (Stanford)<br />
|[[#Jonathan Luk | TBA ]]<br />
| Kim<br />
|-<br />
|March 18,<br />
| Spring recess (Mar 16-24, 2019)<br />
|[[# | ]]<br />
| <br />
|- <br />
|April 1 <br />
| Zaher Hani (Michigan)<br />
|[[#Zaher Hani | TBA ]]<br />
| Ifrim<br />
|-<br />
|April 15,<br />
| Yao Yao (Gatech)<br />
|[[#Yao Yao | TBA ]]<br />
| Tran<br />
|- <br />
|April 22,<br />
| Jessica Lin (McGill University)<br />
|[[#Jessica Lin | TBA ]]<br />
| Tran<br />
|- <br />
|April 29,<br />
| Beomjun Choi (Columbia)<br />
|[[# | TBA ]]<br />
| Angenent<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Julian Lopez-Gomez===<br />
<br />
Title: The theorem of characterization of the Strong Maximum Principle<br />
<br />
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.<br />
<br />
===Hiroyoshi Mitake===<br />
Title: On approximation of time-fractional fully nonlinear equations<br />
<br />
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.) <br />
<br />
<br />
<br />
===Changyou Wang===<br />
<br />
Title: Some recent results on mathematical analysis of Ericksen-Leslie System<br />
<br />
Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.<br />
<br />
===Matthew Schrecker===<br />
<br />
Title: Finite energy methods for the 1D isentropic Euler equations<br />
<br />
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.<br />
<br />
===Anna Mazzucato===<br />
<br />
Title: On the vanishing viscosity limit in incompressible flows<br />
<br />
Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.<br />
<br />
===Lei Wu===<br />
<br />
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects<br />
<br />
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.<br />
<br />
<br />
===Annalaura Stingo===<br />
<br />
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D<br />
<br />
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms » .<br />
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.<br />
<br />
===Yeon-Eung Kim===<br />
<br />
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties<br />
<br />
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.<br />
<br />
===Albert Ai===<br />
<br />
Title: Low Regularity Solutions for Gravity Water Waves<br />
<br />
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.<br />
<br />
===Trevor Leslie===<br />
<br />
Title: Flocking Models with Singular Interaction Kernels<br />
<br />
Abstract: Many biological systems exhibit the property of self-organization, the defining feature of which is coherent, large-scale motion arising from underlying short-range interactions between the agents that make up the system. In this talk, we give an overview of some simple models that have been used to describe the so-called flocking phenomenon. Within the family of models that we consider (of which the Cucker-Smale model is the canonical example), writing down the relevant set of equations amounts to choosing a kernel that governs the interaction between agents. We focus on the recent line of research that treats the case where the interaction kernel is singular. In particular, we discuss some new results on the wellposedness and long-time dynamics of the Euler Alignment model and the Shvydkoy-Tadmor model.<br />
<br />
===Serena Federico===<br />
<br />
Title: Sufficient conditions for local solvability of some degenerate partial differential operators <br />
<br />
Abstract: In this talk we will give sufficient conditions for the local solvability of a class of degenerate second order linear partial differential operators with smooth coefficients. The class under consideration, inspired by some generalizations of the Kannai operator, is characterized by the presence of a complex subprincipal symbol. By giving suitable conditions on the subprincipal part and using the technique of a priori estimates, we will show that the operators in the class are at least $L^2$ to $L^2$ locally solvable.<br />
<br />
===Max Engelstein===<br />
<br />
Title: The role of Energy in Regularity<br />
<br />
Abstract: The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy.<br />
<br />
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field.<br />
<br />
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur.</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15133Research at UW-Madison in DifferentialEquations2018-02-15T19:30:24Z<p>Angenent: /* Faculty in related areas */</p>
<hr />
<div>==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] (Moscow State University, 1982) Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
==Faculty in related areas==<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denisov] (Moscow State University, 1999) Analysis, PDE<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin, 1998) Mixing in fluids, optimization of mixing.<br />
<br />
[http://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie] (Courant Institute, 2008) Fluid dynamics, complex fluids, soft matter, computation.<br />
<br />
[http://www.math.wisc.edu/~stechmann/ Sam Stechmann] (Courant Institute, 2008) Applied math and atmospheric science.<br />
<br />
[http://www.math.wisc.edu/~jin/ Shi Jin] (University of Arizona, 1991) Numerical and applied analysis of hyperbolic conservation laws, kinetic theory, Hamilton-Jacobi equations and front propagations, computational fluid dynamics, quantum dynamics, high frequency waves, and uncertainty quantification.<br />
<br />
[http://www.math.wisc.edu/~qinli/ Qin Li] (UW Madison, 2013) Numerical analysis and scientific computing.<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15132Research at UW-Madison in DifferentialEquations2018-02-15T13:48:24Z<p>Angenent: /* Faculty in related areas */</p>
<hr />
<div>==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] (Moscow State University, 1982) Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
==Faculty in related areas==<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denisov] (Moscow State University, 1999) Analysis, PDE<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin, 1998) Mixing in fluids, optimization of mixing.<br />
<br />
[http://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie] (Courant Institute, 2008) Fluid dynamics, complex fluids, soft matter, computation.<br />
<br />
[http://www.math.wisc.edu/~jin/ Shi Jin] (University of Arizona, 1991) Numerical and applied analysis of hyperbolic conservation laws, kinetic theory, Hamilton-Jacobi equations and front propagations, computational fluid dynamics, quantum dynamics, high frequency waves, and uncertainty quantification.<br />
<br />
[http://www.math.wisc.edu/~qinli/ Qin Li] (UW Madison, 2013) Numerical analysis and scientific computing.<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15131Research at UW-Madison in DifferentialEquations2018-02-14T21:26:56Z<p>Angenent: /* Faculty */</p>
<hr />
<div>==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] (Moscow State University, 1982) Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
==Faculty in related areas==<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denisov] (Moscow State University, 1999) Analysis, PDE<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin, 1998) Mixing in fluids, optimization of mixing.<br />
<br />
[http://www.math.wisc.edu/~jin/ Shi Jin] (University of Arizona, 1991) Numerical and applied analysis of hyperbolic conservation laws, kinetic theory, Hamilton-Jacobi equations and front propagations, computational fluid dynamics, quantum dynamics, high frequency waves, and uncertainty quantification.<br />
<br />
[http://www.math.wisc.edu/~qinli/ Qin Li] (UW Madison, 2013) Numerical analysis and scientific computing.<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15130Research at UW-Madison in DifferentialEquations2018-02-14T21:25:12Z<p>Angenent: /* Faculty in related areas */</p>
<hr />
<div>==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
==Faculty in related areas==<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denisov] (Moscow State University, 1999) Analysis, PDE<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin, 1998) Mixing in fluids, optimization of mixing.<br />
<br />
[http://www.math.wisc.edu/~jin/ Shi Jin] (University of Arizona, 1991) Numerical and applied analysis of hyperbolic conservation laws, kinetic theory, Hamilton-Jacobi equations and front propagations, computational fluid dynamics, quantum dynamics, high frequency waves, and uncertainty quantification.<br />
<br />
[http://www.math.wisc.edu/~qinli/ Qin Li] (UW Madison, 2013) Numerical analysis and scientific computing.<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15129Research at UW-Madison in DifferentialEquations2018-02-14T19:56:04Z<p>Angenent: /* Faculty in related areas */</p>
<hr />
<div>==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
==Faculty in related areas==<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denisov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15128Research at UW-Madison in DifferentialEquations2018-02-14T19:48:55Z<p>Angenent: </p>
<hr />
<div>==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
==Faculty in related areas==<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15127Research at UW-Madison in DifferentialEquations2018-02-14T19:47:27Z<p>Angenent: </p>
<hr />
<div>= Research at UW-Madison in Differential Equations =<br />
<br />
==Seminars of interest==<br />
<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
==Faculty==<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
==Faculty in related areas==<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
==Emeriti==<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15126Research at UW-Madison in DifferentialEquations2018-02-14T19:46:19Z<p>Angenent: </p>
<hr />
<div>= Research at UW-Madison in Differential Equations =<br />
<br />
==Seminars of interest==<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
==Upcoming events==<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15125Research at UW-Madison in DifferentialEquations2018-02-14T19:45:48Z<p>Angenent: </p>
<hr />
<div>= Research at UW-Madison in Differential Equations =<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Upcoming events===<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15124Research at UW-Madison in DifferentialEquations2018-02-14T19:45:04Z<p>Angenent: /* Upcoming events */</p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Upcoming events===<br />
This spring the '''[https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar]''' will be held in Madison on April 21/22 (2018).<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15123Research at UW-Madison in DifferentialEquations2018-02-14T19:44:26Z<p>Angenent: /* Seminars of interest */</p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that will feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Upcoming events===<br />
This spring the [https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar] will be held in Madison on April 21/22 (2018).<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15122Research at UW-Madison in DifferentialEquations2018-02-14T19:43:09Z<p>Angenent: /* Upcoming events */</p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that regularly feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Upcoming events===<br />
This spring the [https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar] will be held in Madison on April 21/22 (2018).<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15121Research at UW-Madison in DifferentialEquations2018-02-14T19:42:21Z<p>Angenent: /* Research at UW-Madison in Differential Equations */</p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that regularly feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Upcoming events===<br />
This spring the [https://sites.google.com/view/81stmidwestpdeseminar/home Midwest PDE seminar] will be held in Madison. <br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15120Research at UW-Madison in DifferentialEquations2018-02-14T19:39:01Z<p>Angenent: /* Faculty */</p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that regularly feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergey Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15119Research at UW-Madison in DifferentialEquations2018-02-14T19:37:20Z<p>Angenent: /* Seminars of interest */</p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars that regularly feature PDE related material are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergei Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15118Research at UW-Madison in DifferentialEquations2018-02-14T19:36:17Z<p>Angenent: </p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
===Seminars of interest===<br />
The weekly [http://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE & Geometric Analysis seminar] is held on Monday afternoons, 3:30-4:30pm. <br />
<br />
Other seminars of interest are the [http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar Geometry and Topology seminar], <br />
the [https://www.math.wisc.edu/wiki/index.php/Analysis_Seminar Analysis seminar], and the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math seminar].<br />
<br />
===Faculty===<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergei Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15116Research at UW-Madison in DifferentialEquations2018-02-14T19:29:56Z<p>Angenent: </p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
'''Faculty'''<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] (UC Berkeley, 2012) Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] (Brown, 2011) Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] (UC Davis, 2012) Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] (UC Berkeley, 1994) Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergei Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent] (Leiden, 1986)<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT, 2011) Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison, 2008) Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] (Moscow State University, 2011) Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15115Research at UW-Madison in DifferentialEquations2018-02-14T19:15:30Z<p>Angenent: </p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
'''Faculty'''<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] Nonlinear PDE<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergei Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent]<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15114Research at UW-Madison in DifferentialEquations2018-02-14T19:14:00Z<p>Angenent: </p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
'''Faculty'''<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent]<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergei Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] Nonlinear PDE<br />
<br />
<br />
'''Faculty in related areas'''<br />
<br />
[https://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] Geometric Analysis, Mean Curvature Flow<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[http://www.math.wisc.edu/~denissov Sergey Denissov] Analysis, PDE<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15113Research at UW-Madison in DifferentialEquations2018-02-14T19:07:04Z<p>Angenent: </p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
'''Faculty'''<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent]<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergei Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] Nonlinear PDE<br />
<br />
<br />
'''Faculty in related areas'''<br />
[Lu Wang] Geometric Analysis, Mean Curvature Flow<br />
<br />
[Bing Wang] Geometric Analysis, Ricci flow, Kaehler-Ricci flow, Mean Curvature flow<br />
<br />
[Sergey Denissov] <br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Research_at_UW-Madison_in_DifferentialEquations&diff=15112Research at UW-Madison in DifferentialEquations2018-02-14T18:18:15Z<p>Angenent: </p>
<hr />
<div>== Research at UW-Madison in Differential Equations ==<br />
<br />
'''Faculty'''<br />
<br />
[http://www.math.wisc.edu/~angenent Sigurd Angenent]<br />
Nonlinear PDE, differential geometry, medical imaging, math biology.<br />
<br />
[http://www.math.wisc.edu/~bolotin Sergei Bolotin] Dynamical Systems, Variational Methods, Celestial Mechanics.<br />
<br />
[http://www.math.wisc.edu/~feldman Mikhail Feldman] Nonlinear PDE, Calculus of Variations<br />
<br />
[http://www.math.wisc.edu/~ifrim/Home.html Mihaela Ifrim] Nonlinear Dispersive Equations (water-wave equations and related dispersive models), Fluid Mechanics, Elastodynamics, Harmonic Analysis, General Relativity.<br />
<br />
[http://www.math.wisc.edu/~ckim Chanwoo Kim] Applied PDE, Kinetic theory, Fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~hung Hung Vinh Tran] Nonlinear PDE<br />
<br />
<br />
'''Emeriti'''<br />
<br />
[http://www.math.wisc.edu/~rabinowi Paul Rabinowitz]<br />
PDE, Calculus of Variations, Dynanamical Systems, Nonlinear Analysis<br />
<br />
[http://www.math.wisc.edu/~robbin Joel Robbin]<br />
Global Analysis, Differential Equations<br />
<br />
[http://www.math.wisc.edu/~turner Robert Turner]<br />
Partial Differential Equations, Fluid Mechanics, Mathematical Biology</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=14630Colloquia/Fall182017-12-02T01:58:50Z<p>Angenent: /* Mathematics Colloquium */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| Adhesion dynamics and the sticky particle system]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Leslie Smith<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | TBA ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Title: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: Adhesion dynamics and the sticky particle system.<br />
<br />
Abstract: The sticky particle system expresses the conservation of mass and<br />
momentum for a collection of particles that only interact via perfectly inelastic collisions. <br />
The equations were first considered in astronomy in a model for the expansion of <br />
matter without pressure. These equations also play a central role in the theory of optimal <br />
transport. Namely, the geodesics in an appropriately metrized space of probability <br />
measures correspond to solutions of the sticky particle system. We will survey what is <br />
known about solutions and discuss connections with Hamilton-Jacobi equations. <br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=14595Colloquia/Fall182017-11-26T22:29:51Z<p>Angenent: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Spring_2018&diff=14576Spring 20182017-11-21T21:00:05Z<p>Angenent: /* Dan Knopf */</p>
<hr />
<div>== PDE GA Seminar Schedule Spring 2018 ==<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 />
|January 29<br />
| Dan Knopf (UT Austin)<br />
|[[#Dan Knopf | Non-K&auml;hler Ricci flow singularities that converge to K&auml;hler-Ricci solitons]]<br />
| Angenent<br />
|- <br />
|February 5<br />
| Andreas Seeger (UW)<br />
|[[#Andreas Seeger | TBD ]]<br />
| Kim & Tran<br />
|- <br />
|February 19<br />
| Maja Taskovic (UPenn)<br />
|[[#Maja Taskovic | TBD ]]<br />
| Kim<br />
|- <br />
|March 5<br />
| Khai Nguyen (NCSU)<br />
|[[#Khai Nguyen | TBD ]]<br />
| Tran<br />
|- <br />
|April 21-22 (Saturday-Sunday)<br />
| Midwest PDE seminar<br />
|[[#Midwest PDE seminar | ]]<br />
| Angenent, Feldman, Kim, Tran.<br />
|- <br />
|April 25 (Wednesday)<br />
| Hitoshi Ishii (Wasow lecture)<br />
|[[#Hitoshi Ishii | TBD]]<br />
| Tran.<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Dan Knopf===<br />
<br />
Title: Non-K&auml;hler Ricci flow singularities that converge to K&auml;hler-Ricci solitons<br />
<br />
Abstract: We describe Riemannian (non-K&auml;hler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking K&auml;hler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-K&auml;hler solutions of Ricci flow that become asymptotically K&auml;hler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of K&auml;hler metrics under Ricci flow.</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Spring_2018&diff=14575Spring 20182017-11-21T20:58:54Z<p>Angenent: /* PDE GA Seminar Schedule Spring 2018 */</p>
<hr />
<div>== PDE GA Seminar Schedule Spring 2018 ==<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 />
|January 29<br />
| Dan Knopf (UT Austin)<br />
|[[#Dan Knopf | Non-K&auml;hler Ricci flow singularities that converge to K&auml;hler-Ricci solitons]]<br />
| Angenent<br />
|- <br />
|February 5<br />
| Andreas Seeger (UW)<br />
|[[#Andreas Seeger | TBD ]]<br />
| Kim & Tran<br />
|- <br />
|February 19<br />
| Maja Taskovic (UPenn)<br />
|[[#Maja Taskovic | TBD ]]<br />
| Kim<br />
|- <br />
|March 5<br />
| Khai Nguyen (NCSU)<br />
|[[#Khai Nguyen | TBD ]]<br />
| Tran<br />
|- <br />
|April 21-22 (Saturday-Sunday)<br />
| Midwest PDE seminar<br />
|[[#Midwest PDE seminar | ]]<br />
| Angenent, Feldman, Kim, Tran.<br />
|- <br />
|April 25 (Wednesday)<br />
| Hitoshi Ishii (Wasow lecture)<br />
|[[#Hitoshi Ishii | TBD]]<br />
| Tran.<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Dan Knopf===<br />
<br />
Title: Non-Kahler Ricci flow singularities that converge to Kahler-Ricci solitons<br />
<br />
Abstract: We describe Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking Kahler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-Kahler solutions of Ricci flow that become asymptotically Kahler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of Kahler metrics under Ricci flow.</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Spring_2018&diff=14574Spring 20182017-11-21T20:56:00Z<p>Angenent: </p>
<hr />
<div>== PDE GA Seminar Schedule Spring 2018 ==<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 />
|January 29<br />
| Dan Knopf (UT Austin)<br />
|[[#Dan Knopf | Non-Kahler Ricci flow singularities that converge to Kahler-Ricci solitons]]<br />
| Angenent<br />
|- <br />
|February 5<br />
| Andreas Seeger (UW)<br />
|[[#Andreas Seeger | TBD ]]<br />
| Kim & Tran<br />
|- <br />
|February 19<br />
| Maja Taskovic (UPenn)<br />
|[[#Maja Taskovic | TBD ]]<br />
| Kim<br />
|- <br />
|March 5<br />
| Khai Nguyen (NCSU)<br />
|[[#Khai Nguyen | TBD ]]<br />
| Tran<br />
|- <br />
|April 21-22 (Saturday-Sunday)<br />
| Midwest PDE seminar<br />
|[[#Midwest PDE seminar | ]]<br />
| Angenent, Feldman, Kim, Tran.<br />
|- <br />
|April 25 (Wednesday)<br />
| Hitoshi Ishii (Wasow lecture)<br />
|[[#Hitoshi Ishii | TBD]]<br />
| Tran.<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Dan Knopf===<br />
<br />
Title: Non-Kahler Ricci flow singularities that converge to Kahler-Ricci solitons<br />
<br />
Abstract: We describe Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking Kahler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-Kahler solutions of Ricci flow that become asymptotically Kahler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of Kahler metrics under Ricci flow.</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Spring_2018&diff=14573Spring 20182017-11-21T20:52:57Z<p>Angenent: /* PDE GA Seminar Schedule Spring 2018 */</p>
<hr />
<div>== PDE GA Seminar Schedule Spring 2018 ==<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 />
|January 29<br />
| Dan Knopf (UT Austin)<br />
|[[#Dan Knopf | Non-Kahler Ricci flow singularities that converge to Kahler-Ricci solitons]]<br />
| Angenent<br />
|- <br />
|February 5<br />
| Andreas Seeger (UW)<br />
|[[#Andreas Seeger | TBD ]]<br />
| Kim & Tran<br />
|- <br />
|February 19<br />
| Maja Taskovic (UPenn)<br />
|[[#Maja Taskovic | TBD ]]<br />
| Kim<br />
|- <br />
|March 5<br />
| Khai Nguyen (NCSU)<br />
|[[#Khai Nguyen | TBD ]]<br />
| Tran<br />
|- <br />
|April 21-22 (Saturday-Sunday)<br />
| Midwest PDE seminar<br />
|[[#Midwest PDE seminar | ]]<br />
| Angenent, Feldman, Kim, Tran.<br />
|- <br />
|April 25 (Wednesday)<br />
| Hitoshi Ishii (Wasow lecture)<br />
|[[#Hitoshi Ishii | TBD]]<br />
| Tran.<br />
|}</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=14571Colloquia/Fall182017-11-20T23:08:17Z<p>Angenent: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in <br />
algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=14570Colloquia/Fall182017-11-20T21:43:06Z<p>Angenent: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in <br />
algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=14526Colloquia/Fall182017-11-10T22:10:25Z<p>Angenent: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, B239<br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|-<br />
|November 3<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Wednesday)<br />
| Ryan Hynd (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| Connor Mooney (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Angenenthttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=14525Colloquia/Fall182017-11-10T22:06:51Z<p>Angenent: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, B239<br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|-<br />
|November 3<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5<br />
| Ryan Hynd (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11<br />
| Connor Mooney (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Angenent