https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Zlatos&feedformat=atomUW-Math Wiki - User contributions [en]2022-12-06T01:00:32ZUser contributionsMediaWiki 1.35.6https://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10920PDE Geometric Analysis seminar2016-01-06T21:22:31Z<p>Zlatos: </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 2016 | Tentative schedule for Fall 2016]]===<br />
<br />
= Seminar Schedule Spring 2016 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 25<br />
||Tianling Jin (HKUST and Caltech)<br />
|[[# Tianling Jin | Holder gradient estimates for parabolic homogeneous p-Laplacian equations ]]<br />
| Zlatos<br />
|-<br />
|February 1<br />
|Russell Schwab (Michigan State University)<br />
|[[# Russell Schwab | TBA ]]<br />
| Lin<br />
|-<br />
|February 8 <br />
|Jingrui Cheng (UW Madison)<br />
|[[# Jingrui Cheng | ]]<br />
|<br />
|-<br />
|February 15 <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|February 22 <br />
| Hong Zhang (Brown)<br />
|[[# Hong Zhang | ]]<br />
| Kim<br />
|-<br />
|February 29<br />
|Aaron Yip (Purdue university) <br />
|[[# Aaron Yip | TBD ]]<br />
| Tran<br />
|-<br />
|March 7<br />
|Hiroyoshi Mitake (Hiroshima university) <br />
||[[# Hiroyoshi Mitake | TBD ]]<br />
| Tran<br />
|-<br />
|March 15<br />
| Nestor Guillen (UMass Amherst)<br />
|[[#Nestor Guillen | TBA ]]<br />
| Lin<br />
|-<br />
|March 21 (Spring Break)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|March 28<br />
| Ryan Denlinger (Courant Institute)<br />
|[[#Ryan Denlinger | TBA ]]<br />
| Lee<br />
|-<br />
|April 4<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|April 11<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 18<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 25<br />
| Moon-Jin Kang (UT-Austin)<br />
|[[# | ]]<br />
| Kim<br />
|-<br />
|May 2<br />
| <br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Tianling Jin===<br />
<br />
Holder gradient estimates for parabolic homogeneous p-Laplacian equations<br />
<br />
We prove interior Holder estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous p-Laplacian equation <br />
u_t=|\nabla u|^{2-p} div(|\nabla u|^{p-2}\nabla u),<br />
where 1<p<\infty. This equation arises from tug-of-war like stochastic games with white noise. It can also be considered as the parabolic p-Laplacian equation in non divergence form. This is joint work with Luis Silvestre.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10919PDE Geometric Analysis seminar2016-01-06T21:22:07Z<p>Zlatos: </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 2016 | Tentative schedule for Fall 2016]]===<br />
<br />
= Seminar Schedule Spring 2016 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 25<br />
||Tianling Jin (HKUST and Caltech)<br />
|[[# Tianling Jin | Holder gradient estimates for parabolic homogeneous p-Laplacian equations ]]<br />
| Zlatos<br />
|-<br />
|February 1<br />
|Russell Schwab (Michigan State University)<br />
|[[# Russell Schwab | TBA ]]<br />
| Lin<br />
|-<br />
|February 8 <br />
|Jingrui Cheng (UW Madison)<br />
|[[# Jingrui Cheng | ]]<br />
|<br />
|-<br />
|February 15 <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|February 22 <br />
| Hong Zhang (Brown)<br />
|[[# Hong Zhang | ]]<br />
| Kim<br />
|-<br />
|February 29<br />
|Aaron Yip (Purdue university) <br />
|[[# Aaron Yip | TBD ]]<br />
| Tran<br />
|-<br />
|March 7<br />
|Hiroyoshi Mitake (Hiroshima university) <br />
||[[# Hiroyoshi Mitake | TBD ]]<br />
| Tran<br />
|-<br />
|March 15<br />
| Nestor Guillen (UMass Amherst)<br />
|[[#Nestor Guillen | TBA ]]<br />
| Lin<br />
|-<br />
|March 21 (Spring Break)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|March 28<br />
| Ryan Denlinger (Courant Institute)<br />
|[[#Ryan Denlinger | TBA ]]<br />
| Lee<br />
|-<br />
|April 4<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|April 11<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 18<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 25<br />
| Moon-Jin Kang (UT-Austin)<br />
|[[# | ]]<br />
| Kim<br />
|-<br />
|May 2<br />
| <br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Tianling Jin===<br />
<br />
Holder gradient estimates for parabolic homogeneous p-Laplacian equations<br />
<br />
We prove interior Holder estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous p-Laplacian equation <br />
$u_t=|\nabla u|^{2-p} div(|\nabla u|^{p-2}\nabla u)$,<br />
where 1<p<\infty. This equation arises from tug-of-war like stochastic games with white noise. It can also be considered as the parabolic p-Laplacian equation in non divergence form. This is joint work with Luis Silvestre.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10918PDE Geometric Analysis seminar2016-01-06T21:21:12Z<p>Zlatos: </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 2016 | Tentative schedule for Fall 2016]]===<br />
<br />
= Seminar Schedule Spring 2016 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 25<br />
||Tianling Jin (HKUST)<br />
|[[# Tianling Jin | Holder gradient estimates for parabolic homogeneous p-Laplacian equations ]]<br />
| Zlatos<br />
|-<br />
|February 1<br />
|Russell Schwab (Michigan State University)<br />
|[[# Russell Schwab | TBA ]]<br />
| Lin<br />
|-<br />
|February 8 <br />
|Jingrui Cheng (UW Madison)<br />
|[[# Jingrui Cheng | ]]<br />
|<br />
|-<br />
|February 15 <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|February 22 <br />
| Hong Zhang (Brown)<br />
|[[# Hong Zhang | ]]<br />
| Kim<br />
|-<br />
|February 29<br />
|Aaron Yip (Purdue university) <br />
|[[# Aaron Yip | TBD ]]<br />
| Tran<br />
|-<br />
|March 7<br />
|Hiroyoshi Mitake (Hiroshima university) <br />
||[[# Hiroyoshi Mitake | TBD ]]<br />
| Tran<br />
|-<br />
|March 15<br />
| Nestor Guillen (UMass Amherst)<br />
|[[#Nestor Guillen | TBA ]]<br />
| Lin<br />
|-<br />
|March 21 (Spring Break)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|March 28<br />
| Ryan Denlinger (Courant Institute)<br />
|[[#Ryan Denlinger | TBA ]]<br />
| Lee<br />
|-<br />
|April 4<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|April 11<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 18<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 25<br />
| Moon-Jin Kang (UT-Austin)<br />
|[[# | ]]<br />
| Kim<br />
|-<br />
|May 2<br />
| <br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
=Abstract=<br />
<br />
===Tianling Jin===<br />
<br />
Holder gradient estimates for parabolic homogeneous p-Laplacian equations<br />
<br />
We prove interior Holder estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous p-Laplacian equation <br />
$$<br />
u_t=|\nabla u|^{2-p} div(|\nabla u|^{p-2}\nabla u),<br />
$$<br />
where 1<p<\infty. This equation arises from tug-of-war like stochastic games with white noise. It can also be considered as the parabolic p-Laplacian equation in non divergence form. This is joint work with Luis Silvestre.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10917PDE Geometric Analysis seminar2016-01-06T21:19:07Z<p>Zlatos: </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 2016 | Tentative schedule for Fall 2016]]===<br />
<br />
= Seminar Schedule Spring 2016 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 25<br />
||Tianling Jin (HKUST)<br />
|[[# Tianling Jin | Holder gradient estimates for parabolic homogeneous p-Laplacian equations ]]<br />
| Zlatos<br />
|-<br />
|February 1<br />
|Russell Schwab (Michigan State University)<br />
|[[# Russell Schwab | TBA ]]<br />
| Lin<br />
|-<br />
|February 8 <br />
|Jingrui Cheng (UW Madison)<br />
|[[# Jingrui Cheng | ]]<br />
|<br />
|-<br />
|February 15 <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|February 22 <br />
| Hong Zhang (Brown)<br />
|[[# Hong Zhang | ]]<br />
| Kim<br />
|-<br />
|February 29<br />
|Aaron Yip (Purdue university) <br />
|[[# Aaron Yip | TBD ]]<br />
| Tran<br />
|-<br />
|March 7<br />
|Hiroyoshi Mitake (Hiroshima university) <br />
||[[# Hiroyoshi Mitake | TBD ]]<br />
| Tran<br />
|-<br />
|March 15<br />
| Nestor Guillen (UMass Amherst)<br />
|[[#Nestor Guillen | TBA ]]<br />
| Lin<br />
|-<br />
|March 21 (Spring Break)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|March 28<br />
| Ryan Denlinger (Courant Institute)<br />
|[[#Ryan Denlinger | TBA ]]<br />
| Lee<br />
|-<br />
|April 4<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|April 11<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 18<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 25<br />
| Moon-Jin Kang (UT-Austin)<br />
|[[# | ]]<br />
| Kim<br />
|-<br />
|May 2<br />
| <br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
=Abstract=<br />
<br />
===Tianling Jin===</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10857PDE Geometric Analysis seminar2015-12-11T02:34:58Z<p>Zlatos: </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 />
===[[Spring 2016 | Tentative schedule for Spring 2016]]===<br />
<br />
<br />
<br />
= Seminar Schedule Fall 2015 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 7 (Labor Day)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|September 14 (special room: B115)<br />
| Hung Tran (Madison)<br />
|[[#Hung Tran | Some inverse problems in periodic homogenization of Hamilton--Jacobi equations ]]<br />
| <br />
|- <br />
|September 21 (special room: B115) <br />
| Eric Baer (Madison)<br />
||[[#Eric Baer | Optimal function spaces for continuity of the Hessian determinant as a distribution ]]<br />
| <br />
|-<br />
|September 28<br />
| Donghyun Lee (Madison)<br />
|[[#Donghyun Lee | FLUIDS WITH FREE-SURFACE AND VANISHING VISCOSITY LIMIT]]<br />
| <br />
|-<br />
|October 5 <br />
|Hyung-Ju Hwang (Postech & Brown Univ)<br />
|[[#Hyung-Ju Hwang | The Fokker-Planck equation in bounded domains ]]<br />
| Kim<br />
|-<br />
|October 12<br />
| Minh-Binh Tran (Madison)<br />
|[[#Minh-Binh Tran | Nonlinear approximation theory for kinetic equations ]]<br />
| <br />
|-<br />
|October 19<br />
| Bob Jensen (Loyola University Chicago)<br />
||[[#Bob Jensen | Crandall-Lions Viscosity Solutions of Uniformly Elliptic PDEs ]]<br />
| Tran<br />
|-<br />
|October 26<br />
|Luis Silvestre (Chicago)<br />
|[[#Luis Silvestre | A priori estimates for integral equations and the Boltzmann equation ]]<br />
|Kim<br />
|-<br />
|November 2<br />
| Connor Mooney (UT Austin)<br />
|[[#Connor Mooney | Counterexamples to Sobolev regularity for degenerate Monge-Ampere equations ]]<br />
|Lin<br />
|-<br />
|November 9<br />
| Javier Gomez Serrano (Princeton)<br />
||[[#Javier Gomez Serrano | Existence and regularity of rotating global solutions for active scalars ]]<br />
|Zlatos<br />
|-<br />
|November 16<br />
| Yifeng Yu (UC Irvine)<br />
|[[#Yifeng Yu | G-equation in the modeling of flame propagation ]]<br />
| Tran<br />
|-<br />
|November 23<br />
| Nam Le (Indiana)<br />
|[[#Nam Le | Global smoothness of the Monge-Ampere eigenfunctions ]]<br />
|Tran<br />
|-<br />
|November 30<br />
| Qin Li (Madison)<br />
|[[#Qin Li | Kinetic-fluid coupling: transition from the Boltzmann to the Euler ]]<br />
|<br />
|-<br />
|December 7<br />
| Lu Wang (Madison) <br />
||[[#Lu Wang | Asymptotic Geometry of Self-shrinkers ]]<br />
|<br />
|-<br />
|December 14<br />
| Christophe Lacave (Paris 7)<br />
|[[# Christophe Lacave | Well-posedness for 2D Euler in non-smooth domains ]]<br />
| Zlatos<br />
|}<br />
<br />
=Abstract=<br />
<br />
===Hung Tran===<br />
<br />
Some inverse problems in periodic homogenization of Hamilton--Jacobi equations.<br />
<br />
Abstract: We look at the effective Hamiltonian $\overline{H}$ associated with the Hamiltonian $H(p,x)=H(p)+V(x)$ in the periodic homogenization theory. Our central goal is to understand the relation between $V$ and $\overline{H}$. We formulate some inverse problems concerning this relation. Such type of inverse problems are in general very challenging. I will discuss some interesting cases in both convex and nonconvex settings. Joint work with Songting Luo and Yifeng Yu.<br />
<br />
<br />
===Eric Baer===<br />
<br />
Optimal function spaces for continuity of the Hessian determinant as a distribution.<br />
<br />
Abstract: In this talk we describe a new class of optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\mathbb{R}^N$, obtained in collaboration with D. Jerison. Inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space $B(2-2/N,N)$ of fractional order, and that all continuity results in this scale of Besov spaces are consequences of this result. A key ingredient in the argument is the characterization of $B(2-2/N,N)$ as the space of traces of functions in the Sobolev space $W^{2,N}(\mathbb{R}^{N+2})$ on the subspace $\mathbb{R}^N$ (of codimension 2). The most elaborate part of the analysis is the construction of a counterexample to continuity in $B(2-2/N,p)$ with $p>N$. Tools involved in this step include the choice of suitable ``atoms" having a tensor product structure and Hessian determinant of uniform sign, formation of lacunary series of rescaled atoms, and delicate estimates of terms in the resulting multilinear expressions.<br />
<br />
===Donghyun Lee===<br />
<br />
FLUIDS WITH FREE-SURFACE AND VANISHING VISCOSITY LIMIT.<br />
<br />
Abstract : Free-boundary problems of incompressible fluids have been studied for several decades. In the viscous case, it is basically solved by Stokes regularity. However, the inviscid case problem is generally much harder, because the problem is purely hyperbolic. In this talk, we approach the problem via vanishing viscosity limit, which is a central problem of fluid mechanics. To correct boundary layer behavior, conormal Sobolev space will be introduced. In the spirit of the recent work by N.Masmoudi and F.Rousset (2012, non-surface tension), we will see how to get local regularity of incompressible free-boundary Euler, taking surface tension into account. This is joint work with Tarek Elgindi.<br />
If possible, we also talk about applying the similar technique to the free-boundary MHD(Magnetohydrodynamics). Especially, we will see that strong zero initial boundary condition is still valid for this coupled PDE. For the general boundary condition (for perfect conductor), however, the problem is still open.<br />
<br />
===Hyung-Ju Hwang===<br />
<br />
The Fokker-Planck equation in bounded domains<br />
<br />
abstract: In this talk, we consider the initial-boundary value problem for the Fokker-Planck equation in an interval or in a bounded domain with absorbing boundary conditions. We discuss a theory of well-posedness of classical solutions for the problem as well as the exponential decay in time, hypoellipticity away from the singular set, and the Holder continuity of the solutions up to the singular set. This is a joint work with J. Jang, J. Jung, and J. Velazquez.<br />
<br />
===Minh-Binh Tran===<br />
<br />
Nonlinear approximation theory for kinetic equations<br />
<br />
Abstract: Numerical resolution methods for the Boltzmann equation plays a very important role in the practical a theoretical study of the theory of rarefied gas. The main difficulty in the approximation of the Boltzmann equation is due to the multidimensional structure of the Boltzmann collision operator. The major problem with deterministic numerical methods using to solve Boltzmann equation is that we have to truncate the domain or to impose nonphysical conditions to keep the supports of the solutions in the velocity space uniformly compact. I<br />
n this talk, we will introduce our new way to make the connection between nonlinear approximation theory and kinetic theory. Our nonlinear wavelet approximation is nontruncated and based on an adaptive spectral method associated with a new wavelet filtering technique. The approximation is proved to converge and preserve many properties of the homogeneous Boltzmann equation. The nonlinear approximation solves the equation without having to impose non-physics conditions on the equation.<br />
<br />
===Bob Jensen===<br />
<br />
Crandall-Lions Viscosity Solutions of Uniformly Elliptic PDEs<br />
<br />
Abstract: I will discuss C-L viscosity solutions of uniformly elliptic partial differential equations for operators with only measurable spatial regularity. E.g., $L[u] = \sum a_{i\,j}(x)\,D_{i\,j}u(x)$ where $a_{i\,j}(x)$ is bounded, uniformly elliptic, and measurable in $x$. In general there isn't a meaningful extension of the C-L viscosity solution definition to operators with measurable spatial dependence. But under uniform ellipticity there is a natural extension. Though there isn't a general comparison principle in this context, we will see that the extended definition is robust and uniquely characterizes the ``right" solutions for such problems.<br />
<br />
===Luis Silvestre===<br />
<br />
A priori estimates for integral equations and the Boltzmann equation.<br />
<br />
Abstract: We will review some results on the regularity of general parabolic integro-differential equations. We will see how these results can be applied in order to obtain a priori estimates for the Boltzmann equation (without cutoff) modelling the evolution of particle density in a dilute gas. We derive a bound in L^infinity for the full Boltzmann equation, and Holder continuity estimates in the space homogeneous case.<br />
<br />
===Connor Mooney===<br />
<br />
Counterexamples to Sobolev regularity for degenerate Monge-Ampere equations<br />
<br />
Abstract: W^{2,1} estimates for the Monge-Ampere equation \det D^2u = f in R^n were first obtained by De Philippis and Figalli in the case that f is bounded between positive constants. Motivated by applications to the semigeostrophic equation, we consider the case that f is bounded but allowed to be zero on some set. In this case there are simple counterexamples to W^{2,1} regularity in dimension n \geq 3 that have a Lipschitz singularity. In contrast, if n = 2 a classical theorem of Alexandrov on the propagation of Lipschitz singularities shows that solutions are C^1. We will discuss a counterexample to W^{2,1} regularity in two dimensions whose second derivatives have nontrivial Cantor part, and also a related result on the propagation of Lipschitz / log(Lipschitz) singularities that is optimal by example.<br />
<br />
===Javier Gomez Serrano===<br />
<br />
Existence and regularity of rotating global solutions for active scalars<br />
<br />
A particular kind of weak solutions for a 2D active scalar equation are the so called patches, i.e., solutions for which the scalar is a step function taking one value inside a moving region and another in the complement. The evolution of such distribution is completely determined by the evolution of the boundary, allowing the problem to be treated as a non-local one dimensional equation for the contour. In this talk we will discuss the existence and regularity of uniformly rotating solutions for the vortex patch and generalized surface quasi-geostrophic (gSQG) patch equation. We will also outline the proof for the smooth (non patch) SQG case. Joint work with Angel Castro and Diego Cordoba.<br />
<br />
===Yifeng Yu===<br />
<br />
G-equation in the modeling of flame propagation.<br />
<br />
Abstract: G-equation is a well known model in turbulent combustion. In<br />
this talk, I will present joint works with Jack Xin about how the<br />
effective burning velocity (turbulent flame speed) depends on the strength<br />
of the ambient fluid (e.g. the speed of the wind) under various G-equation<br />
model.<br />
<br />
===Nam Le===<br />
<br />
Global smoothness of the Monge-Ampere eigenfunctions<br />
<br />
Abstract:<br />
In this talk, I will discuss global smoothness of the eigenfunctions of the Monge-Ampere operator on smooth, bounded and uniformly convex domains in all dimensions. A key ingredient in our analysis is boundary Schauder estimates for certain degenerate Monge-Ampere equations. This is joint work with Ovidiu Savin.<br />
<br />
===Qin Li===<br />
<br />
Kinetic-fluid coupling: transition from the Boltzmann to the Euler<br />
<br />
Abstract: Kinetic equations (the Boltzmann, the neutron transport equation etc.) are known to converge to fluid equations (the Euler, the heat equation etc.) in certain regimes, but when kinetic and fluid regime co-exist, how to couple the two systems remains an open problem. The key is to understand the half-space problem that resembles the boundary layer at the interface. In this talk, I will present a unified proof for the well-posedness of a class of half-space equations with general incoming data, propose an efficient spectral solver, and utilize it to couple fluid with kinetics. Moreover, I will present complete error analysis for the proposed spectral solver. Numerical results will be shown to demonstrate the accuracy of the algorithm.<br />
<br />
===Lu Wang===<br />
<br />
Asymptotic Geometry of Self-shrinkers<br />
<br />
Abstract: In this talk, we will discuss some recent progress towards the conjectural asymptotic behaviors of two-dimensional self-shrinkers of mean curvature flow.<br />
<br />
===Christophe Lacave===<br />
<br />
Well-posedness for 2D Euler in non-smooth domains<br />
<br />
The well-posedness of the Euler system has been of course the matter of many works, but a common point in all the previous studies is that the boundary is at least $C^{1,1}$. In a first part, we will establish the existence of global weak solutions of the 2D incompressible Euler equations for a large class of non-smooth open sets. Existence of weak solutions with $L^p$ vorticity is deduced from an approximation argument, that relates to the so-called $\gamma$-convergence of domains. In a second part, we will prove the uniqueness if the open set is the interior or the exterior of a simply connected domain, where the boundary has a finite number of corners. Although the velocity blows up near these corners, we will get a similar theorem to the Yudovich's result. Theses works are in collaboration with David Gerard-Varet, Evelyne Miot and Chao Wang.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10636PDE Geometric Analysis seminar2015-11-05T16:02:53Z<p>Zlatos: </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 />
===[[Spring 2016 | Tentative schedule for Spring 2016]]===<br />
<br />
<br />
<br />
= Seminar Schedule Fall 2015 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 7 (Labor Day)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|September 14 (special room: B115)<br />
| Hung Tran (Madison)<br />
|[[#Hung Tran | Some inverse problems in periodic homogenization of Hamilton--Jacobi equations ]]<br />
| <br />
|- <br />
|September 21 (special room: B115) <br />
| Eric Baer (Madison)<br />
||[[#Eric Baer | Optimal function spaces for continuity of the Hessian determinant as a distribution ]]<br />
| <br />
|-<br />
|September 28<br />
| Donghyun Lee (Madison)<br />
|[[#Donghyun Lee | FLUIDS WITH FREE-SURFACE AND VANISHING VISCOSITY LIMIT]]<br />
| <br />
|-<br />
|October 5 <br />
|Hyung-Ju Hwang (Postech & Brown Univ)<br />
|[[#Hyung-Ju Hwang | The Fokker-Planck equation in bounded domains ]]<br />
| Kim<br />
|-<br />
|October 12<br />
| Minh-Binh Tran (Madison)<br />
|[[#Minh-Binh Tran | Nonlinear approximation theory for kinetic equations ]]<br />
| <br />
|-<br />
|October 19<br />
| Bob Jensen (Loyola University Chicago)<br />
||[[#Bob Jensen | Crandall-Lions Viscosity Solutions of Uniformly Elliptic PDEs ]]<br />
| Tran<br />
|-<br />
|October 26<br />
|Luis Silvestre (Chicago)<br />
|[[# Luis Silvestre | A priori estimates for integral equations and the Boltzmann equation ]]<br />
|Kim<br />
|-<br />
|November 2<br />
| Connor Mooney (UT Austin)<br />
|[[# Connor Mooney | Counterexamples to Sobolev regularity for degenerate Monge-Ampere equations ]]<br />
|Lin<br />
|-<br />
|November 9<br />
| Javier Gomez Serrano (Princeton)<br />
||[[# Javier Gomez-Serrano | Existence and regularity of rotating global solutions for active scalars ]]<br />
|Zlatos<br />
|-<br />
|November 16<br />
| Yifeng Yu (UC Irvine)<br />
|[[# Yifeng Yu | TBA ]]<br />
| Tran<br />
|-<br />
|November 23<br />
| Nam Le (Indiana)<br />
|[[# Nam Le | TBA ]]<br />
|Tran<br />
|-<br />
|November 30<br />
| Qin Li (Madison)<br />
|[[# Qin Li | TBA ]]<br />
|<br />
|-<br />
|December 7<br />
| Lu Wang (Madison)<br />
||[[# Lu Wang | TBA ]]<br />
|<br />
|-<br />
|December 14<br />
| Christophe Lacave (Paris 7)<br />
|[[# Christophe Lacave | TBA ]]<br />
| Zlatos<br />
|}<br />
<br />
=Abstract=<br />
<br />
===Hung Tran===<br />
<br />
Some inverse problems in periodic homogenization of Hamilton--Jacobi equations.<br />
<br />
Abstract: We look at the effective Hamiltonian $\overline{H}$ associated with the Hamiltonian $H(p,x)=H(p)+V(x)$ in the periodic homogenization theory. Our central goal is to understand the relation between $V$ and $\overline{H}$. We formulate some inverse problems concerning this relation. Such type of inverse problems are in general very challenging. I will discuss some interesting cases in both convex and nonconvex settings. Joint work with Songting Luo and Yifeng Yu.<br />
<br />
<br />
===Eric Baer===<br />
<br />
Optimal function spaces for continuity of the Hessian determinant as a distribution.<br />
<br />
Abstract: In this talk we describe a new class of optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\mathbb{R}^N$, obtained in collaboration with D. Jerison. Inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space $B(2-2/N,N)$ of fractional order, and that all continuity results in this scale of Besov spaces are consequences of this result. A key ingredient in the argument is the characterization of $B(2-2/N,N)$ as the space of traces of functions in the Sobolev space $W^{2,N}(\mathbb{R}^{N+2})$ on the subspace $\mathbb{R}^N$ (of codimension 2). The most elaborate part of the analysis is the construction of a counterexample to continuity in $B(2-2/N,p)$ with $p>N$. Tools involved in this step include the choice of suitable ``atoms" having a tensor product structure and Hessian determinant of uniform sign, formation of lacunary series of rescaled atoms, and delicate estimates of terms in the resulting multilinear expressions.<br />
<br />
===Donghyun Lee===<br />
<br />
FLUIDS WITH FREE-SURFACE AND VANISHING VISCOSITY LIMIT.<br />
<br />
Abstract : Free-boundary problems of incompressible fluids have been studied for several decades. In the viscous case, it is basically solved by Stokes regularity. However, the inviscid case problem is generally much harder, because the problem is purely hyperbolic. In this talk, we approach the problem via vanishing viscosity limit, which is a central problem of fluid mechanics. To correct boundary layer behavior, conormal Sobolev space will be introduced. In the spirit of the recent work by N.Masmoudi and F.Rousset (2012, non-surface tension), we will see how to get local regularity of incompressible free-boundary Euler, taking surface tension into account. This is joint work with Tarek Elgindi.<br />
If possible, we also talk about applying the similar technique to the free-boundary MHD(Magnetohydrodynamics). Especially, we will see that strong zero initial boundary condition is still valid for this coupled PDE. For the general boundary condition (for perfect conductor), however, the problem is still open.<br />
<br />
=== Hyung-Ju Hwang===<br />
<br />
The Fokker-Planck equation in bounded domains<br />
<br />
abstract: In this talk, we consider the initial-boundary value problem for the Fokker-Planck equation in an interval or in a bounded domain with absorbing boundary conditions. We discuss a theory of well-posedness of classical solutions for the problem as well as the exponential decay in time, hypoellipticity away from the singular set, and the Holder continuity of the solutions up to the singular set. This is a joint work with J. Jang, J. Jung, and J. Velazquez.<br />
<br />
=== Minh-Binh Tran ===<br />
<br />
Nonlinear approximation theory for kinetic equations<br />
<br />
Abstract: Numerical resolution methods for the Boltzmann equation plays a very important role in the practical a theoretical study of the theory of rarefied gas. The main difficulty in the approximation of the Boltzmann equation is due to the multidimensional structure of the Boltzmann collision operator. The major problem with deterministic numerical methods using to solve Boltzmann equation is that we have to truncate the domain or to impose nonphysical conditions to keep the supports of the solutions in the velocity space uniformly compact. I<br />
n this talk, we will introduce our new way to make the connection between nonlinear approximation theory and kinetic theory. Our nonlinear wavelet approximation is nontruncated and based on an adaptive spectral method associated with a new wavelet filtering technique. The approximation is proved to converge and preserve many properties of the homogeneous Boltzmann equation. The nonlinear approximation solves the equation without having to impose non-physics conditions on the equation.<br />
<br />
=== Bob Jensen ===<br />
<br />
Crandall-Lions Viscosity Solutions of Uniformly Elliptic PDEs<br />
<br />
Abstract: I will discuss C-L viscosity solutions of uniformly elliptic partial differential equations for operators with only measurable spatial regularity. E.g., $L[u] = \sum a_{i\,j}(x)\,D_{i\,j}u(x)$ where $a_{i\,j}(x)$ is bounded, uniformly elliptic, and measurable in $x$. In general there isn't a meaningful extension of the C-L viscosity solution definition to operators with measurable spatial dependence. But under uniform ellipticity there is a natural extension. Though there isn't a general comparison principle in this context, we will see that the extended definition is robust and uniquely characterizes the ``right" solutions for such problems.<br />
<br />
===Luis Silvestre===<br />
<br />
A priori estimates for integral equations and the Boltzmann equation.<br />
<br />
Abstract: We will review some results on the regularity of general parabolic integro-differential equations. We will see how these results can be applied in order to obtain a priori estimates for the Boltzmann equation (without cutoff) modelling the evolution of particle density in a dilute gas. We derive a bound in L^infinity for the full Boltzmann equation, and Holder continuity estimates in the space homogeneous case.<br />
<br />
=== Connor Mooney ===<br />
<br />
Counterexamples to Sobolev regularity for degenerate Monge-Ampere equations<br />
<br />
Abstract: W^{2,1} estimates for the Monge-Ampere equation \det D^2u = f in R^n were first obtained by De Philippis and Figalli in the case that f is bounded between positive constants. Motivated by applications to the semigeostrophic equation, we consider the case that f is bounded but allowed to be zero on some set. In this case there are simple counterexamples to W^{2,1} regularity in dimension n \geq 3 that have a Lipschitz singularity. In contrast, if n = 2 a classical theorem of Alexandrov on the propagation of Lipschitz singularities shows that solutions are C^1. We will discuss a counterexample to W^{2,1} regularity in two dimensions whose second derivatives have nontrivial Cantor part, and also a related result on the propagation of Lipschitz / log(Lipschitz) singularities that is optimal by example.<br />
<br />
=== Javier Gomez Serrano ===<br />
<br />
Existence and regularity of rotating global solutions for active scalars<br />
<br />
A particular kind of weak solutions for a 2D active scalar equation are the so called patches, i.e., solutions for which the scalar is a step function taking one value inside a moving region and another in the complement. The evolution of such distribution is completely determined by the evolution of the boundary, allowing the problem to be treated as a non-local one dimensional equation for the contour. In this talk we will discuss the existence and regularity of uniformly rotating solutions for the vortex patch and generalized surface quasi-geostrophic (gSQG) patch equation. We will also outline the proof for the smooth (non patch) SQG case. Joint work with Angel Castro and Diego Cordoba.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Spring_2016&diff=10592Spring 20162015-10-29T04:53:36Z<p>Zlatos: </p>
<hr />
<div>= Seminar Schedule Spring 2016 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 25<br />
||Tianling Jin (HKUST)<br />
|[[# Tianling Jin | TBA ]]<br />
| Zlatos<br />
|-<br />
|February 1<br />
|Russell Schwab (Michigan State University)<br />
|[[# Russell Schwab | TBA ]]<br />
| Lin<br />
|-<br />
|February 8 <br />
|<br />
|[[# | ]]<br />
|<br />
|-<br />
|February 15<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|February 22 <br />
|<br />
|[[# | ]]<br />
|<br />
|-<br />
|February 29<br />
|Aaron Yip (Purdue university) <br />
|[[# Aaron Yip | TBD ]]<br />
| Tran<br />
|-<br />
|March 7<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|March 15<br />
| Nestor Guillen (UMass Amherst)<br />
|[[#Nestor Guillen | TBA ]]<br />
| Lin<br />
|-<br />
|March 21 (Spring Break)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|March 28<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 4<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|April 11<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 18<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 25<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|May 2<br />
| <br />
|[[# | ]]<br />
|</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Spring_2016&diff=10591Spring 20162015-10-29T04:53:16Z<p>Zlatos: </p>
<hr />
<div>= Seminar Schedule Spring 2016 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 25<br />
| <br />
||Tianling Jin (HKUST)<br />
|[[# Tianling Jin | TBA ]]<br />
| Zlatos<br />
|-<br />
|February 1<br />
|Russell Schwab (Michigan State University)<br />
|[[# Russell Schwab | TBA ]]<br />
| Lin<br />
|-<br />
|February 8 <br />
|<br />
|[[# | ]]<br />
|<br />
|-<br />
|February 15<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|February 22 <br />
|<br />
|[[# | ]]<br />
|<br />
|-<br />
|February 29<br />
|Aaron Yip (Purdue university) <br />
|[[# Aaron Yip | TBD ]]<br />
| Tran<br />
|-<br />
|March 7<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|March 15<br />
| Nestor Guillen (UMass Amherst)<br />
|[[#Nestor Guillen | TBA ]]<br />
| Lin<br />
|-<br />
|March 21 (Spring Break)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|March 28<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 4<br />
| <br />
||[[# | ]]<br />
| <br />
|-<br />
|April 11<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 18<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|April 25<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|May 2<br />
| <br />
|[[# | ]]<br />
|</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10271PDE Geometric Analysis seminar2015-09-21T17:23:27Z<p>Zlatos: /* Seminar Schedule Fall 2015 */</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 />
===[[Spring 2016 | Tentative schedule for Spring 2016]]===<br />
<br />
<br />
<br />
= Seminar Schedule Fall 2015 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 7 (Labor Day)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|September 14 (special room: B115)<br />
| Hung Tran (Madison)<br />
|[[#Hung Tran | Some inverse problems in periodic homogenization of Hamilton--Jacobi equations ]]<br />
| <br />
|- <br />
|September 21 (special room: B115) <br />
| Eric Baer (Madison)<br />
||[[#Eric Baer | Optimal function spaces for continuity of the Hessian determinant as a distribution ]]<br />
| <br />
|-<br />
|September 28<br />
| Donghyun Lee (Madison)<br />
|[[# Donghyun Lee |TBA ]]<br />
| <br />
|-<br />
|October 5 <br />
|Hyung-Ju Hwang (Postech & Brown Univ)<br />
|[[# Hyung-Ju Hwang | TBA ]]<br />
| Kim<br />
|-<br />
|October 12<br />
| Binh Tran (Madison)<br />
|[[# Binh Tran | TBA ]]<br />
| <br />
|-<br />
|October 19<br />
| Bob Jensen (Loyola University Chicago)<br />
||[[# Bob Jensen | TBA ]]<br />
| Tran<br />
|-<br />
|October 26<br />
|Luis Silvestre (Chicago)<br />
|[[# Luis Silvestre | TBA ]]<br />
|Kim<br />
|-<br />
|November 2<br />
| Connor Mooney (UT Austin)<br />
|[[# Connor Mooney | TBA ]]<br />
|Lin<br />
|-<br />
|November 9<br />
| Javier Gomez-Serrano (Princeton)<br />
||[[# Javier Gomez-Serrano | TBA ]]<br />
|Zlatos<br />
|-<br />
|November 16<br />
| Yifeng Yu (UC Irvine)<br />
|[[# Yifeng Yu | TBA ]]<br />
| Tran<br />
|-<br />
|November 23<br />
| Nam Le (Indiana)<br />
|[[# Nam Le | TBA ]]<br />
|Tran<br />
|-<br />
|November 30<br />
| Lu Wang (Madison)<br />
||[[# Lu Wang | TBA ]]<br />
|<br />
|-<br />
|December 7<br />
| Qin Li (Madison)<br />
|[[# Qin Li | TBA ]]<br />
|<br />
|-<br />
|December 14<br />
| Christophe Lacave (Paris 7)<br />
|[[# Christophe Lacave | TBA ]]<br />
| Zlatos<br />
|}<br />
<br />
=Abstract=<br />
<br />
===Hung Tran===<br />
<br />
Some inverse problems in periodic homogenization of Hamilton--Jacobi equations.<br />
<br />
Abstract: We look at the effective Hamiltonian $\overline{H}$ associated with the Hamiltonian $H(p,x)=H(p)+V(x)$ in the periodic homogenization theory. Our central goal is to understand the relation between $V$ and $\overline{H}$. We formulate some inverse problems concerning this relation. Such type of inverse problems are in general very challenging. I will discuss some interesting cases in both convex and nonconvex settings. Joint work with Songting Luo and Yifeng Yu.<br />
<br />
<br />
===Eric Baer===<br />
<br />
Optimal function spaces for continuity of the Hessian determinant as a distribution.<br />
<br />
Abstract: In this talk we describe a new class of optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\mathbb{R}^N$, obtained in collaboration with D. Jerison. Inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space $B(2-2/N,N)$ of fractional order, and that all continuity results in this scale of Besov spaces are consequences of this result. A key ingredient in the argument is the characterization of $B(2-2/N,N)$ as the space of traces of functions in the Sobolev space $W^{2,N}(\mathbb{R}^{N+2})$ on the subspace $\mathbb{R}^N$ (of codimension 2). The most elaborate part of the analysis is the construction of a counterexample to continuity in $B(2-2/N,p)$ with $p>N$. Tools involved in this step include the choice of suitable ``atoms" having a tensor product structure and Hessian determinant of uniform sign, formation of lacunary series of rescaled atoms, and delicate estimates of terms in the resulting multilinear expressions.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10254PDE Geometric Analysis seminar2015-09-18T19:21:47Z<p>Zlatos: </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 />
===[[Spring 2016 | Tentative schedule for Spring 2016]]===<br />
<br />
<br />
<br />
= Seminar Schedule Fall 2015 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 7 (Labor Day)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|September 14 (special room: B115)<br />
| Hung Tran (Madison)<br />
|[[#Hung Tran | Some inverse problems in periodic homogenization of Hamilton--Jacobi equations ]]<br />
| <br />
|- <br />
|September 21 (special room: B115) <br />
| Eric Baer (Madison)<br />
||[[#Eric Baer | Optimal function spaces for continuity of the Hessian determinant as a distribution ]]<br />
| <br />
|-<br />
|September 28<br />
| Donghyun Lee (Madison)<br />
|[[# Donghyun Lee |TBA ]]<br />
| <br />
|-<br />
|October 5 <br />
|Hyung-Ju Hwang (Postech & Brown Univ)<br />
|[[# Hyung-Ju Hwang | TBA ]]<br />
| Kim<br />
|-<br />
|October 12<br />
| Binh Tran (Madison)<br />
|[[# Binh Tran | TBA ]]<br />
| <br />
|-<br />
|October 19<br />
| Bob Jensen (Loyola University Chicago)<br />
||[[# Bob Jensen | TBA ]]<br />
| Tran<br />
|-<br />
|October 26<br />
|Luis Silvestre (Chicago)<br />
|[[# Luis Silvestre | TBA ]]<br />
|Kim<br />
|-<br />
|November 2<br />
| Connor Mooney (UT Austin)<br />
|[[# Connor Mooney | TBA ]]<br />
|Lin<br />
|-<br />
|November 9<br />
| Javier Gomez-Serrano (Princeton)<br />
||[[# Javier Gomez-Serrano | TBA ]]<br />
|Zlatos<br />
|-<br />
|November 16<br />
| Yifeng Yu (UC Irvine)<br />
|[[# Yifeng Yu | TBA ]]<br />
| Tran<br />
|-<br />
|November 23<br />
| Nam Le (Indiana)<br />
|[[# Nam Le | TBA ]]<br />
|Tran<br />
|-<br />
|November 30<br />
| Lu Wang (Madison)<br />
||[[# Lu Wang | TBA ]]<br />
|<br />
|-<br />
|December 7<br />
| Qin Li (Madison)<br />
|[[# Qin Li | TBA ]]<br />
|<br />
|-<br />
|December 14<br />
| reserved<br />
|[[# | ]]<br />
| Zlatos<br />
|}<br />
<br />
=Abstract=<br />
<br />
===Hung Tran===<br />
<br />
Some inverse problems in periodic homogenization of Hamilton--Jacobi equations.<br />
<br />
Abstract: We look at the effective Hamiltonian $\overline{H}$ associated with the Hamiltonian $H(p,x)=H(p)+V(x)$ in the periodic homogenization theory. Our central goal is to understand the relation between $V$ and $\overline{H}$. We formulate some inverse problems concerning this relation. Such type of inverse problems are in general very challenging. I will discuss some interesting cases in both convex and nonconvex settings. Joint work with Songting Luo and Yifeng Yu.<br />
<br />
<br />
===Eric Baer===<br />
<br />
Optimal function spaces for continuity of the Hessian determinant as a distribution.<br />
<br />
Abstract: In this talk we describe a new class of optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\mathbb{R}^N$, obtained in collaboration with D. Jerison. Inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space $B(2-2/N,N)$ of fractional order, and that all continuity results in this scale of Besov spaces are consequences of this result. A key ingredient in the argument is the characterization of $B(2-2/N,N)$ as the space of traces of functions in the Sobolev space $W^{2,N}(\mathbb{R}^{N+2})$ on the subspace $\mathbb{R}^N$ (of codimension 2). The most elaborate part of the analysis is the construction of a counterexample to continuity in $B(2-2/N,p)$ with $p>N$. Tools involved in this step include the choice of suitable ``atoms" having a tensor product structure and Hessian determinant of uniform sign, formation of lacunary series of rescaled atoms, and delicate estimates of terms in the resulting multilinear expressions.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=10241PDE Geometric Analysis seminar2015-09-18T11:13:41Z<p>Zlatos: /* Seminar Schedule Fall 2015 */</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 />
===[[Spring 2016 | Tentative schedule for Spring 2016]]===<br />
<br />
<br />
<br />
= Seminar Schedule Fall 2015 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 7 (Labor Day)<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|September 14 (special room: B115)<br />
| Hung Tran (Madison)<br />
|[[#Hung Tran | Some inverse problems in periodic homogenization of Hamilton--Jacobi equations ]]<br />
| <br />
|- <br />
|September 21 <br />
| Eric Baer (Madison)<br />
||[[#Eric Baer | Optimal function spaces for continuity of the Hessian determinant as a distribution ]]<br />
| <br />
|-<br />
|September 28<br />
| Donghyun Lee (Madison)<br />
|[[# Donghyun Lee |TBA ]]<br />
| <br />
|-<br />
|October 5 <br />
|Hyung-Ju Hwang (Postech & Brown Univ)<br />
|[[# Hyung-Ju Hwang | TBA ]]<br />
| Kim<br />
|-<br />
|October 12<br />
| Binh Tran (Madison)<br />
|[[# Binh Tran | TBA ]]<br />
| <br />
|-<br />
|October 19<br />
| Bob Jensen (Loyola University Chicago)<br />
||[[# Bob Jensen | TBA ]]<br />
| Tran<br />
|-<br />
|October 26<br />
|Luis Silvestre (Chicago)<br />
|[[# Luis Silvestre | TBA ]]<br />
|Kim<br />
|-<br />
|November 2<br />
| Connor Mooney (UT Austin)<br />
|[[# Connor Mooney | TBA ]]<br />
|Lin<br />
|-<br />
|November 9<br />
| Lu Wang (Madison)<br />
||[[# Lu Wang | TBA ]]<br />
|<br />
|-<br />
|November 16<br />
| Yifeng Yu (UC Irvine)<br />
|[[# Yifeng Yu | TBA ]]<br />
| Tran<br />
|-<br />
|November 23<br />
| Nam Le (Indiana)<br />
|[[# Nam Le | TBA ]]<br />
|Tran<br />
|-<br />
|November 30<br />
| Qin Li (Madison)<br />
|[[# Qin Li | TBA ]]<br />
|<br />
|-<br />
|December 7<br />
| reserved<br />
|[[# | ]]<br />
| Zlatos<br />
|-<br />
|December 14<br />
| reserved<br />
|[[# | ]]<br />
| Zlatos<br />
|}<br />
<br />
=Abstract=<br />
<br />
===Hung Tran===<br />
<br />
Some inverse problems in periodic homogenization of Hamilton--Jacobi equations.<br />
<br />
Abstract: We look at the effective Hamiltonian $\overline{H}$ associated with the Hamiltonian $H(p,x)=H(p)+V(x)$ in the periodic homogenization theory. Our central goal is to understand the relation between $V$ and $\overline{H}$. We formulate some inverse problems concerning this relation. Such type of inverse problems are in general very challenging. I will discuss some interesting cases in both convex and nonconvex settings. Joint work with Songting Luo and Yifeng Yu.<br />
<br />
<br />
===Eric Baer===<br />
<br />
Optimal function spaces for continuity of the Hessian determinant as a distribution.<br />
<br />
Abstract: In this talk we describe a new class of optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\mathbb{R}^N$, obtained in collaboration with D. Jerison. Inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space $B(2-2/N,N)$ of fractional order, and that all continuity results in this scale of Besov spaces are consequences of this result. A key ingredient in the argument is the characterization of $B(2-2/N,N)$ as the space of traces of functions in the Sobolev space $W^{2,N}(\mathbb{R}^{N+2})$ on the subspace $\mathbb{R}^N$ (of codimension 2). The most elaborate part of the analysis is the construction of a counterexample to continuity in $B(2-2/N,p)$ with $p>N$. Tools involved in this step include the choice of suitable ``atoms" having a tensor product structure and Hessian determinant of uniform sign, formation of lacunary series of rescaled atoms, and delicate estimates of terms in the resulting multilinear expressions.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=9661PDE Geometric Analysis seminar2015-04-14T19:32:42Z<p>Zlatos: </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 2015 | Tentative schedule for Fall 2015]]===<br />
<br />
= Seminar Schedule Spring 2015 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21 (Departmental Colloquium: 4PM, B239) <br />
|Jun Kitagawa (Toronto) <br />
|[[#Jun Kitagawa (Toronto) | Regularity theory for generated Jacobian equations: from optimal transport to geometric optics ]]<br />
|Feldman <br />
|-<br />
|February 9 <br />
|Jessica Lin (Madison)<br />
|[[#Jessica Lin (Madison) | Algebraic Error Estimates for the Stochastic Homogenization of Uniformly Parabolic Equations ]]<br />
|Kim<br />
|-<br />
|February 17 (Tuesday) (joint with Analysis Seminar: 4PM, B139)<br />
|Chanwoo Kim (Madison) <br />
|[[#Chanwoo Kim (Madison) | Hydrodynamic limit from the Boltzmann to the Navier-Stokes-Fourier ]]<br />
|Seeger <br />
|-<br />
|February 23 (special time*, '''3PM, B119''') <br />
| Yaguang Wang (Shanghai Jiao Tong)<br />
|[[ #Yaguang Wang | Stability of Three-dimensional Prandtl Boundary Layers ]]<br />
|Jin<br />
|-<br />
|March 2 <br />
|Benoit Pausader (Princeton)<br />
|[[#Benoit Pausader (Princeton) | Global smooth solutions for the Euler-Maxwell problem for electrons in 2 dimensions]]<br />
|Kim<br />
|-<br />
|March 9 <br />
|Haozhao Li (University of Science and Technology of China) <br />
|[[#Haozhao Li|Regularity scales and convergence of the Calabi flow]]<br />
|Wang <br />
|-<br />
|March 16 <br />
| Jennifer Beichman (Madison) <br />
|[[#Jennifer Beichman (Madison) |Nonstandard dispersive estimates and linearized water waves ]]<br />
| Kim<br />
|-<br />
|March 23 <br />
| Ben Fehrman (University of Chicago)<br />
|[[#Ben Fehrman (University of Chicago) | On The Existence of an Invariant Measure for Isotropic Diffusions in Random Environments ]]<br />
| Lin<br />
|-<br />
|March 30 <br />
| Spring recess Mar 28-Apr 5 (S-N)<br />
|[[# | ]]<br />
| <br />
|-<br />
|April 13 <br />
| Sung-Jin Oh (Berkeley)<br />
|[[# Berkeley | Global well-posedness of the energy critical Maxwell-Klein-Gordon equation ]]<br />
| Kim<br />
|-<br />
|April 20 <br />
|Yuan Lou (Ohio State)<br />
|[[#Yuan Lou (Ohio State) | Asymptotic behavior of the smallest eigenvalue of an elliptic operator and its applications to evolution of dispersal]]<br />
|Zlatos<br />
|-<br />
|April 27 <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|April 28 (a joint seminar with analysis, 4:00 p.m B139)<br />
| Diego Córdoba (ICMAT, Madrid) <br />
|[[# | ]]<br />
| Zlatos<br />
|-<br />
|May 4 tentative<br />
| Vera Hur (UIUC) tentative<br />
|[[# Vera Hur (UIUC) |Instabilities in nonlinear dispersive waves ]]<br />
| Yao<br />
|-<br />
|}<br />
<br />
<br />
== Abstracts ==<br />
<br />
===Jun Kitagawa (Toronto)===<br />
<br />
Regularity theory for generated Jacobian equations: from optimal transport to geometric optics<br />
<br />
Equations of Monge-Ampere type arise in numerous contexts, and solutions often exhibit very subtle qualitative and quantitative properties; this is owing to the highly nonlinear nature of the equation, and its degeneracy (in the sense of ellipticity). Motivated by an example from geometric optics, I will talk about the class of Generated Jacobian Equations; recently introduced by Trudinger, this class also encompasses, for example, optimal transport, the Minkowski problem, and the classical Monge-Ampere equation. I will present a new regularity result for weak solutions of these equations, which is new even in the case of equations arising from near-field reflector problems (of interest from a physical and practical point of view). This talk is based on joint works with N. Guillen.<br />
<br />
===Jessica Lin (Madison)===<br />
<br />
Algebraic Error Estimates for the Stochastic Homogenization of Uniformly Parabolic Equations<br />
<br />
We establish error estimates for the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media. Based on the approach of Armstrong and Smart in the elliptic setting, we construct a quantity which captures the geometric behavior of solutions to parabolic equations. The error estimates are shown to be of algebraic order. This talk is based on joint work with Charles Smart.<br />
<br />
<br />
===Yaguang Wang (Shanghai Jiao Tong)===<br />
<br />
Stability of Three-dimensional Prandtl Boundary Layers<br />
<br />
In this talk, we shall study the stability of the Prandtl boundary layer<br />
equations in three space variables. First, we obtain a well-posedness<br />
result of the three-dimensional Prandtl equations under some constraint on<br />
its flow structure. It reveals that the classical Burgers equation plays an<br />
important role in determining this type of flow with special structure,<br />
that avoids the appearance of the complicated secondary flow in the<br />
three-dimensional Prandtl boundary layers. Second, we give an instability<br />
criterion for the Prandtl equations in three space variables. Both of<br />
linear and nonlinear stability are considered. This criterion shows that<br />
the monotonic shear flow is linearly stable for the three dimensional<br />
Prandtl equations if and only if the tangential velocity field direction is<br />
invariant with respect to the normal variable, which is an exact complement<br />
to the above well-posedness result for a special flow. This is a joint work<br />
with Chengjie Liu and Tong Yang.<br />
<br />
<br />
===Benoit Pausader (Princeton)===<br />
<br />
Global smooth solutions for the Euler-Maxwell problem for electrons in 2 dimensions<br />
<br />
It is well known that pure compressible fluids tend to develop shocks, even from small perturbation. We study how self consistent electromagnetic fields can stabilize these fluids. In a joint work with A. Ionescu and Y. Deng, we consider a compressible fluid of electrons in 2D, subject to its own electromagnetic field and to a field created by a uniform background of positively charged ions. We show that small smooth and irrotational perturbations of a uniform background at rest lead to solutions that remain globally smooth, in contrast with neutral fluids. This amounts to proving small data global existence for a system of quasilinear Klein-Gordon equations with different speeds.<br />
<br />
<br />
===Haozhao Li (University of Science and Technology of China)===<br />
<br />
Regularity scales and convergence of the Calabi flow<br />
<br />
We define regularity scales to study the behavior of the Calabi flow. <br />
Based on estimates of the regularity scales, we obtain convergence theorems<br />
of the Calabi flow on extremal K\"ahler surfaces, under the assumption of global existence<br />
of the Calabi flow solutions. Our results partially confirm Donaldson’s conjectural picture for<br />
the Calabi flow in complex dimension 2. Similar results hold in high dimension with an extra<br />
assumption that the scalar curvature is uniformly bounded.<br />
<br />
<br />
===Jennifer Beichman (UW-Madison)===<br />
<br />
Nonstandard dispersive estimates and linearized water waves<br />
<br />
In this talk, we focus on understanding the relationship between the decay of a solution to the linearized water wave problem and its initial data. We obtain decay bounds for a class of 1D dispersive equations that includes the linearized water wave. These decay bounds display a surprising growth factor, which we show is sharp. A further exploration leads to a result relating singularities of the initial data at the origin in Fourier frequency to the regularity of the solution.<br />
<br />
===Ben Fehrman (University of Chicago)===<br />
<br />
On The Existence of an Invariant Measure for Isotropic Diffusions in Random Environments<br />
<br />
I will discuss the existence of a unique mutually absolutely continuous invariant measure for isotropic diffusions in random environment, of dimension at least three, which are small perturbations of Brownian motion satisfying a finite range dependence. This framework was first considered in the continuous setting by Sznitman and Zeitouni and in the discrete setting by Bricmont and Kupiainen. The results of this talk should be seen as an extension of their work.<br />
<br />
I will furthermore mention applications of this analysis to the stochastic homogenization of the related elliptic and parabolic equations with random oscillatory boundary data and, explain how the existence of an invariant measure can be used to prove a Liouville property for the environment. In the latter case, the methods were motivated by work in the discrete setting by Benjamini, Duminil-Copin, Kozma and Yadin.<br />
<br />
===Vera Hur=== <br />
<br />
Instabilities in nonlinear dispersive waves<br />
<br />
I will speak on the wave breaking and the modulational instability of nonlinear wave trains in dispersive media. I will begin by a gradient blowup proof for the Boussinesq-Whitham equations for water waves. I will then describe a variational approach to determine instability to long wavelength perturbations for a general class of Hamiltonian systems, allowing for nonlocal dispersion. I will discuss KdV type equations with fractional dispersion in depth. Lastly, I will explain an asymptotics approach for Whitham's equation for water waves, qualitatively reproducing the Benjamin-Feir instability of Stokes waves.<br />
<br />
===Sung-Jin Oh=== <br />
<br />
Global well-posedness of the energy critical Maxwell-Klein-Gordon equation<br />
<br />
The massless Maxwell-Klein-Gordon system describes the interaction between an electromagnetic field (Maxwell) and a charged massless scalar field (massless Klein-Gordon, or wave). <br />
In this talk, I will present a recent proof, joint with D. Tataru, of global well-posedness and scattering of this system for arbitrary finite energy data in the (4+1)-dimensional Minkowski space, in which the PDE is energy critical.<br />
<br />
===Yuan Lou=== <br />
<br />
Asymptotic behavior of the smallest eigenvalue of an elliptic operator and its applications to evolution of dispersal<br />
<br />
We investigate the effects of diffusion and drift on the smallest eigenvalue of an elliptic operator with zero Neumann boundary condition. Various asymptotic behaviors of the smallest eigenvalue, as diffusion and drift rates approach zero or infinity, are derived. As an application, these qualitative results yield some insight into the evolution of dispersal in heterogeneous environments.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Spring_2015&diff=8584Spring 20152014-10-11T14:55:53Z<p>Zlatos: </p>
<hr />
<div>===[[PDE Geometric Analysis seminar|PDE Geometric Analysis seminar]]===<br />
<br />
= Seminar Schedule Spring 2015 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|March 2 <br />
|Benoit Pausader (Princeton)<br />
|[[#Benoit Pausader (Princeton) | TBA]]<br />
|C.Kim<br />
|-<br />
|April 20 <br />
|Yuan Lou (Ohio State)<br />
|[[#Yuan Lou (Ohio State) | TBA]]<br />
|Zlatos<br />
|-<br />
|}<br />
<br />
<br />
== Abstracts ==</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8058Analysis2014-08-23T14:52:58Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Our research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars], [http://www.math.wisc.edu/~seeger/pastconf.html Conferences], Other Activities==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m. in B139 Van Vleck Hall. Here is a list of [http://www.math.wisc.edu/~seeger/pastsem.html past seminars].<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
[http://www.math.wisc.edu/apam/ RTG in Analysis and Applications]<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br><br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Beichman.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~beichman Jennifer Beichman]<br><br />
University of Michigan, 2013<br><br />
Van Vleck Assistant Professor<br><br />
beichman at math.wisc.edu<br />
<br />
[[Image:Benguria.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~benguria Soledad Benguria]<br><br />
University of Wisconsin, 2014<br><br />
Van Vleck Assistant Professor<br><br />
benguria at math.wisc.edu<br />
<br />
[[Image:Choi.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kchoi Kyudong Choi]<br><br />
University of Texas, 2012<br><br />
Van Vleck Assistant Professor<br><br />
kchoi at math.wisc.edu<br />
<br />
[[Image:Cook.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~bcook Brian Cook]<br><br />
University of British Columbia, 2010<br><br />
Van Vleck Assistant Professor<br><br />
bcook at math.wisc.edu<br />
<br />
[[Image:Lin.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~jessica Jessica Lin]<br><br />
University of Chicago, 2014<br><br />
Van Vleck Assistant Professor<br><br />
jessica at math.wisc.edu<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8057Analysis2014-08-23T09:50:33Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Our research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars], [http://www.math.wisc.edu/~seeger/pastconf.html Conferences], Other Activities==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m. in B139 Van Vleck Hall. Here is a list of [http://www.math.wisc.edu/~seeger/pastsem.html past seminars].<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
[http://www.math.wisc.edu/apam/ RTG in Analysis and Applications]<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Beichman.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~beichman Jennifer Beichman]<br><br />
University of Michigan, 2013<br><br />
Van Vleck Assistant Professor<br><br />
beichman at math.wisc.edu<br />
<br />
[[Image:Benguria.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~benguria Soledad Benguria]<br><br />
University of Wisconsin, 2014<br><br />
Van Vleck Assistant Professor<br><br />
benguria at math.wisc.edu<br />
<br />
[[Image:Choi.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kchoi Kyudong Choi]<br><br />
University of Texas, 2012<br><br />
Van Vleck Assistant Professor<br><br />
kchoi at math.wisc.edu<br />
<br />
[[Image:Cook.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~bcook Brian Cook]<br><br />
University of British Columbia, 2010<br><br />
Van Vleck Assistant Professor<br><br />
bcook at math.wisc.edu<br />
<br />
[[Image:Lin.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~jessica Jessica Lin]<br><br />
University of Chicago, 2014<br><br />
Van Vleck Assistant Professor<br><br />
jessica at math.wisc.edu<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8056Analysis2014-08-23T09:27:34Z<p>Zlatos: /* Seminars, Conferences, Other Activities */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars], [http://www.math.wisc.edu/~seeger/pastconf.html Conferences], Other Activities==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m. in B139 Van Vleck Hall. Here is a list of [http://www.math.wisc.edu/~seeger/pastsem.html past seminars].<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
[http://www.math.wisc.edu/apam/ RTG in Analysis and Applications]<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Beichman.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~beichman Jennifer Beichman]<br><br />
University of Michigan, 2013<br><br />
Van Vleck Assistant Professor<br><br />
beichman at math.wisc.edu<br />
<br />
[[Image:Benguria.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~benguria Soledad Benguria]<br><br />
University of Wisconsin, 2014<br><br />
Van Vleck Assistant Professor<br><br />
benguria at math.wisc.edu<br />
<br />
[[Image:Choi.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kchoi Kyudong Choi]<br><br />
University of Texas, 2012<br><br />
Van Vleck Assistant Professor<br><br />
kchoi at math.wisc.edu<br />
<br />
[[Image:Cook.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~bcook Brian Cook]<br><br />
University of British Columbia, 2010<br><br />
Van Vleck Assistant Professor<br><br />
bcook at math.wisc.edu<br />
<br />
[[Image:Lin.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~jessica Jessica Lin]<br><br />
University of Chicago, 2014<br><br />
Van Vleck Assistant Professor<br><br />
jessica at math.wisc.edu<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8055Analysis2014-08-23T09:26:46Z<p>Zlatos: /* Postdocs */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars], [http://www.math.wisc.edu/~seeger/pastconf.html Conferences], Other Activities==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m. in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
[http://www.math.wisc.edu/apam/ RTG in Analysis and Applications]<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Beichman.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~beichman Jennifer Beichman]<br><br />
University of Michigan, 2013<br><br />
Van Vleck Assistant Professor<br><br />
beichman at math.wisc.edu<br />
<br />
[[Image:Benguria.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~benguria Soledad Benguria]<br><br />
University of Wisconsin, 2014<br><br />
Van Vleck Assistant Professor<br><br />
benguria at math.wisc.edu<br />
<br />
[[Image:Choi.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kchoi Kyudong Choi]<br><br />
University of Texas, 2012<br><br />
Van Vleck Assistant Professor<br><br />
kchoi at math.wisc.edu<br />
<br />
[[Image:Cook.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~bcook Brian Cook]<br><br />
University of British Columbia, 2010<br><br />
Van Vleck Assistant Professor<br><br />
bcook at math.wisc.edu<br />
<br />
[[Image:Lin.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~jessica Jessica Lin]<br><br />
University of Chicago, 2014<br><br />
Van Vleck Assistant Professor<br><br />
jessica at math.wisc.edu<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8054Analysis2014-08-23T09:17:51Z<p>Zlatos: /* Seminars, Conferences, Other Activities */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars], [http://www.math.wisc.edu/~seeger/pastconf.html Conferences], Other Activities==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m. in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
[http://www.math.wisc.edu/apam/ RTG in Analysis and Applications]<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8053Analysis2014-08-23T09:17:35Z<p>Zlatos: /* Seminars, Conferences, and Other Activities */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars], [http://www.math.wisc.edu/~seeger/pastconf.html Conferences], Other Activities==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
[http://www.math.wisc.edu/apam/ RTG in Analysis and Applications]<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8052Analysis2014-08-23T09:17:20Z<p>Zlatos: /* Seminars and Conferences */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars], [http://www.math.wisc.edu/~seeger/pastconf.html Conferences], and Other Activities==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
[http://www.math.wisc.edu/apam/ RTG in Analysis and Applications]<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8051Analysis2014-08-23T09:14:34Z<p>Zlatos: /* Emeriti */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars] and [http://www.math.wisc.edu/~seeger/pastconf.html Conferences]==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8050Analysis2014-08-23T09:12:42Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Analytic Number Theory <br />
Special Functions <br />
Wavelets<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars] and [http://www.math.wisc.edu/~seeger/pastconf.html Conferences]==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8049Analysis2014-08-23T09:12:14Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Wavelets<br />
Analytic Number Theory <br />
Special Functions <br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars] and [http://www.math.wisc.edu/~seeger/pastconf.html Conferences]==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]<br />
<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8048Analysis2014-08-23T09:11:52Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Wavelets<br />
Analytic Number Theory <br />
Special Functions <br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminars] and [http://www.math.wisc.edu/~seeger/pastconf.html Conferences]==<br />
[https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]==<br />
<br />
[http://www.math.wisc.edu/~kiselev/conference2011.html Madison Springtime Analysis and PDE Workshop]<br />
April 30-May 1, 2011<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8047Analysis2014-08-23T09:10:09Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Wavelets<br />
Analytic Number Theory <br />
Special Functions <br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Analysis Seminar]==<br />
The [https://www.math.wisc.edu/~seeger/curr.html Analysis Seminar] usually meets on Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]==<br />
<br />
[http://www.math.wisc.edu/~kiselev/conference2011.html Madison Springtime Analysis and PDE Workshop]<br />
April 30-May 1, 2011<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Marshall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~marshall Simon Marshall]<br><br />
Princeton University, 2010<br><br />
Assistant Professor<br><br />
marshall at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Stovall.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~stovall Betsy Stovall]<br><br />
UC Berkeley, 2009<br><br />
Assistant Professor<br><br />
stovall at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~zlatos Andrej Zlatoš]<br><br />
Caltech, 2003<br><br />
Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Yao.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~yaoyao Yao Yao]<br><br />
UCLA, 2012<br><br />
Van Vleck Assistant Professor<br><br />
yaoyao at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor Emeritus<br><br />
wainger at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia University, 1971<br><br />
Professor Emeritus<br><br />
nagel at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton University, 1999<br><br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8046Analysis2014-08-23T08:57:14Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations<br />
Mathematical Physics<br />
Approximation Theory<br />
Analysis on Lie groups<br />
Wavelets<br />
Analytic Number Theory <br />
Special Functions <br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminar]==<br />
The seminar will usually meet Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]==<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]==<br />
<br />
[http://www.math.wisc.edu/~kiselev/conference2011.html Madison Springtime Analysis and PDE Workshop]<br />
April 30-May 1, 2011<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Associate Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br><br />
Professor<br><br />
kiselev at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia, 1971<br><br />
Professor<br><br />
nagel at math.wisc.edu<br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
Professor<br><br />
nazarov at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Van Vleck Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
Andrej Zlatoš<br><br />
Caltech, 2003<br><br />
Assistant Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Fish.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~afish Alexander Fish]<br><br />
Hebrew University of Jerusalem, Israel, 2007<br><br />
Van Vleck Assistant Professor<br><br />
afish at math.wisc.edu<br />
<br />
[[Image:LaVictoire.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~patlavic Patrick LaVictoire]<br><br />
University of California (Berkeley), 2010 <br><br />
Van Vleck Assistant Professor<br><br />
patlavic at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor<br><br />
wainger at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton, 1999<br><br />
Professor<br><br />
ionescu at math.princeton.edu</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Analysis&diff=8045Analysis2014-08-23T08:56:27Z<p>Zlatos: </p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis<br />
Harmonic Analysis<br />
Partial Differential Equations, Mathematical Physics,<br />
Approximation Theory, Analysis on Lie groups, Wavelets, Analytic Number Theory, and <br />
Special Functions. <br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminar]==<br />
The seminar will usually meet Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]==<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]==<br />
<br />
[http://www.math.wisc.edu/~kiselev/conference2011.html Madison Springtime Analysis and PDE Workshop]<br />
April 30-May 1, 2011<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Associate Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br><br />
Professor<br><br />
kiselev at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia, 1971<br><br />
Professor<br><br />
nagel at math.wisc.edu<br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
Professor<br><br />
nazarov at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Van Vleck Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
Andrej Zlatoš<br><br />
Caltech, 2003<br><br />
Assistant Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Fish.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~afish Alexander Fish]<br><br />
Hebrew University of Jerusalem, Israel, 2007<br><br />
Van Vleck Assistant Professor<br><br />
afish at math.wisc.edu<br />
<br />
[[Image:LaVictoire.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~patlavic Patrick LaVictoire]<br><br />
University of California (Berkeley), 2010 <br><br />
Van Vleck Assistant Professor<br><br />
patlavic at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor<br><br />
wainger at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton, 1999<br><br />
Professor<br><br />
ionescu at math.princeton.edu</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=6350PDE Geometric Analysis seminar2014-01-14T05:22:25Z<p>Zlatos: </p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
<br />
= Seminar Schedule Fall 2013 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Greg Drugan (U. of Washington)<br />
|[[#Greg Drugan (U. of Washington) |<br />
Construction of immersed self-shrinkers]]<br />
|Angenent<br />
|-<br />
|-<br />
|October 7<br />
|[http://users.cms.caltech.edu/~gluo/ Guo Luo (Caltech)]<br />
|[[#Guo Luo (Caltech) |<br />
Potentially Singular Solutions of the 3D Incompressible Euler Equations. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 18<br />
|[http://people.cas.uab.edu/~shterenb/ Roman Shterenberg (UAB)]<br />
|[[#Roman Shterenberg (UAB) |<br />
Recent progress in multidimensional periodic and almost-periodic spectral<br />
problems. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 25<br />
|Myeongju Chae (Hankyong National University visiting UW)<br />
|[[#Myeongju Chae (Hankyong National University) |<br />
On the global classical solution of the Keller-Segel-Navier -Stokes system and its asymptotic behavior. ]]<br />
|Kiselev<br />
|-<br />
myeongju Chae <br />
|-<br />
|December 2<br />
|Xiaojie Wang<br />
|[[#Xiaojie Wang (Stony Brook University) |<br />
Uniqueness of Ricci flow solutions on noncompact manifolds. ]]<br />
|Wang<br />
|-<br />
|-<br />
|December 16<br />
|Antonio Ache(Princeton)<br />
|[[#Antonio Ache(Princeton) |<br />
Ricci Curvature and the manifold learning problem. NOTE: Due to final exams, this seminar will be held in B231. ]]<br />
|Viaclovsky<br />
|-<br />
|}<br />
<br />
= Seminar Schedule Spring 2014 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 14 at 4pm in B139 (TUESDAY), joint with Analysis<br />
|[http://www.math.univ-toulouse.fr/~roque/ Jean-Michel Roquejoffre (Toulouse)]<br />
|[[#Jean-Michel Roquejoffre (Toulouse) |<br />
Front propagation in the presence of integral diffusion. ]]<br />
|Zlatos<br />
|-<br />
|-<br />
|March 3<br />
|[http://www.dam.brown.edu/people/hdong Hongjie Dong (Brown)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|March 10<br />
|[http://math.uchicago.edu/~jiahao/ Hao Jia (University of Chicago)]<br />
|[[#Hao Jia (University of Chicago) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 7<br />
|[http://pi.math.virginia.edu/~zg7c/ Zoran Grujic (University of Virginia)]<br />
|[[#Zoran Grujic (University of Virginia) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 21<br />
|[http://people.math.gatech.edu/~panrh/ Ronghua Pan (Georgia Tech)]<br />
|[[#Ronghua Pan (Georgia Tech) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
<br />
===Greg Drugan (U. of Washington)===<br />
''Construction of immersed self-shrinkers''<br />
<br />
Abstract: We describe a procedure for constructing immersed<br />
self-shrinking solutions to mean curvature flow. <br />
The self-shrinkers we construct have a rotational symmetry, and<br />
the construction involves a detailed study of geodesics in the<br />
upper-half plane with a conformal metric.<br />
This is a joint work with Stephen Kleene.<br />
<br />
===Guo Luo (Caltech)===<br />
''Potentially Singular Solutions of the 3D Incompressible Euler Equations''<br />
<br />
Abstract:<br />
Whether the 3D incompressible Euler equations can develop a singularity in <br />
finite time from smooth initial data is one of the most challenging problems in <br />
mathematical fluid dynamics. This work attempts to provide an affirmative answer to this <br />
long-standing open question from a numerical point of view, by presenting a class of <br />
potentially singular solutions to the Euler equations computed in axisymmetric <br />
geometries. The solutions satisfy a periodic boundary condition along the axial direction <br />
and no-flow boundary condition on the solid wall. The equations are discretized in space <br />
using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially <br />
designed adaptive (moving) meshes that are dynamically adjusted to the evolving <br />
solutions. With a maximum effective resolution of over $(3 \times 10^{12})^{2}$ near the <br />
point of singularity, we are able to advance the solution up to $\tau_{2} = 0.003505$ and <br />
predict a singularity time of $t_{s} \approx 0.0035056$, while achieving a <br />
\emph{pointwise} relative error of $O(10^{-4})$ in the vorticity vector $\omega$ and <br />
observing a $(3 \times 10^{8})$-fold increase in the maximum vorticity <br />
$\norm{\omega}_{\infty}$. The numerical data is checked against all major blowup <br />
(non-blowup) criteria, including Beale-Kato-Majda, Constantin-Fefferman-Majda, and <br />
Deng-Hou-Yu, to confirm the validity of the singularity. A careful local analysis also <br />
suggests that the blowing-up solution develops a self-similar structure near the point of <br />
the singularity, as the singularity time is approached.<br />
<br />
===Xiaojie Wang(Stony Brook)===<br />
''Uniqueness of Ricci flow solutions on noncompact manifolds''<br />
<br />
Abstract:<br />
Ricci flow is an important evolution equation of Riemannian metrics.<br />
Since it was introduced by R. Hamilton in 1982, it has greatly changed the landscape of riemannian geometry. One of the fundamental question about ricci flow is when is its solution to initial value problem unique. On compact manifold, with arbitrary initial metric, it was confirmed by Hamilton. On noncompact manifold, we only know this is true when further restrictions are imposed to the solution. In this talk, we will discuss various conditions that guarantee the uniqueness. In particular, we will discuss in details with the following uniqueness result. Let $(M,g)$ be a complete noncompact non-collapsing $n$-dimensional riemannian manifold, whose complex sectional curvature is bounded from below and scalar curvature is bounded from above. Then ricci flow with above as its initial data, on $M\times [0,\epsilon]$ for some $\epsilon>0$, has at most one solution in the class of complete riemannian metric with complex sectional curvature bounded from below.<br />
<br />
===Roman Shterenberg(UAB)===<br />
''Recent progress in multidimensional periodic and almost-periodic spectral<br />
problems''<br />
<br />
Abstract: We present a review of the results in multidimensional periodic<br />
and almost-periodic spectral problems. We discuss some recent progress and<br />
old/new ideas used in the constructions. The talk is mostly based on the<br />
joint works with Yu. Karpeshina and L. Parnovski.<br />
<br />
===Antonio Ache(Princeton)===<br />
''Ricci Curvature and the manifold learning problem''<br />
<br />
Abstract: In the first half of this talk we will review several notions of coarse or weak<br />
Ricci Curvature on metric measure spaces which include the works of Lott-Villani, Sturm<br />
and Ollivier. The discussion of the notion of coarse Ricci curvature will serve as <br />
motivation for developing a method to estimate the Ricci curvature of a an embedded<br />
submaifold of Euclidean space from a point cloud which has applications to the Manifold<br />
Learning Problem. Our method is based on combining the notion of ``Carre du Champ"<br />
introduced by Bakry-Emery with a result of Belkin and Niyogi which shows that it is<br />
possible to recover the rough laplacian of embedded submanifolds of the Euclidean space<br />
from point clouds. This is joint work with Micah Warren.<br />
<br />
===Jean-Michel Roquejoffre (Toulouse)===<br />
''Front propagation in the presence of integral diffusion''<br />
<br />
Abstract: In many reaction-diffusion equations, where diffusion is<br />
given by a second order elliptic operator, the solutions<br />
will exhibit spatial transitions whose velocity is asymptotically<br />
linear in time. The situation can be different when the diffusion is of the<br />
integral type, the most basic example being the fractional Laplacian:<br />
the velocity can be time-exponential. We will explain why, and<br />
discuss several situations where this type of fast propagation<br />
occurs.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=6349PDE Geometric Analysis seminar2014-01-14T05:20:43Z<p>Zlatos: </p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
<br />
= Seminar Schedule Fall 2013 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Greg Drugan (U. of Washington)<br />
|[[#Greg Drugan (U. of Washington) |<br />
Construction of immersed self-shrinkers]]<br />
|Angenent<br />
|-<br />
|-<br />
|October 7<br />
|[http://users.cms.caltech.edu/~gluo/ Guo Luo (Caltech)]<br />
|[[#Guo Luo (Caltech) |<br />
Potentially Singular Solutions of the 3D Incompressible Euler Equations. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 18<br />
|[http://people.cas.uab.edu/~shterenb/ Roman Shterenberg (UAB)]<br />
|[[#Roman Shterenberg (UAB) |<br />
Recent progress in multidimensional periodic and almost-periodic spectral<br />
problems. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 25<br />
|Myeongju Chae (Hankyong National University visiting UW)<br />
|[[#Myeongju Chae (Hankyong National University) |<br />
On the global classical solution of the Keller-Segel-Navier -Stokes system and its asymptotic behavior. ]]<br />
|Kiselev<br />
|-<br />
myeongju Chae <br />
|-<br />
|December 2<br />
|Xiaojie Wang<br />
|[[#Xiaojie Wang (Stony Brook University) |<br />
Uniqueness of Ricci flow solutions on noncompact manifolds. ]]<br />
|Wang<br />
|-<br />
|-<br />
|December 16<br />
|Antonio Ache(Princeton)<br />
|[[#Antonio Ache(Princeton) |<br />
Ricci Curvature and the manifold learning problem. NOTE: Due to final exams, this seminar will be held in B231. ]]<br />
|Viaclovsky<br />
|-<br />
|}<br />
<br />
= Seminar Schedule Spring 2014 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 14 at 4pm in B139 (TUESDAY), joint with Analysis<br />
|[http://www.math.univ-toulouse.fr/~roque/ Jean-Michel Roquejoffre (Toulouse)]<br />
|[[#Jean-Michel Roquejoffre (Toulouse) |<br />
Front propagation in the presence of integral diffusion. ]]<br />
|Zlatos<br />
|-<br />
|-<br />
|March 3<br />
|[http://www.dam.brown.edu/people/hdong Hongjie Dong (Brown)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|March 10<br />
|[http://math.uchicago.edu/~jiahao/ Hao Jia (University of Chicago)]<br />
|[[#Hao Jia (University of Chicago) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 7<br />
|[http://pi.math.virginia.edu/~zg7c/ Zoran Grujic (University of Virginia)]<br />
|[[#Zoran Grujic (University of Virginia) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 21<br />
|[http://people.math.gatech.edu/~panrh/ Ronghua Pan (Georgia Tech)]<br />
|[[#Ronghua Pan (Georgia Tech) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
<br />
===Greg Drugan (U. of Washington)===<br />
''Construction of immersed self-shrinkers''<br />
<br />
Abstract: We describe a procedure for constructing immersed<br />
self-shrinking solutions to mean curvature flow. <br />
The self-shrinkers we construct have a rotational symmetry, and<br />
the construction involves a detailed study of geodesics in the<br />
upper-half plane with a conformal metric.<br />
This is a joint work with Stephen Kleene.<br />
<br />
===Guo Luo (Caltech)===<br />
''Potentially Singular Solutions of the 3D Incompressible Euler Equations''<br />
<br />
Abstract:<br />
Whether the 3D incompressible Euler equations can develop a singularity in <br />
finite time from smooth initial data is one of the most challenging problems in <br />
mathematical fluid dynamics. This work attempts to provide an affirmative answer to this <br />
long-standing open question from a numerical point of view, by presenting a class of <br />
potentially singular solutions to the Euler equations computed in axisymmetric <br />
geometries. The solutions satisfy a periodic boundary condition along the axial direction <br />
and no-flow boundary condition on the solid wall. The equations are discretized in space <br />
using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially <br />
designed adaptive (moving) meshes that are dynamically adjusted to the evolving <br />
solutions. With a maximum effective resolution of over $(3 \times 10^{12})^{2}$ near the <br />
point of singularity, we are able to advance the solution up to $\tau_{2} = 0.003505$ and <br />
predict a singularity time of $t_{s} \approx 0.0035056$, while achieving a <br />
\emph{pointwise} relative error of $O(10^{-4})$ in the vorticity vector $\omega$ and <br />
observing a $(3 \times 10^{8})$-fold increase in the maximum vorticity <br />
$\norm{\omega}_{\infty}$. The numerical data is checked against all major blowup <br />
(non-blowup) criteria, including Beale-Kato-Majda, Constantin-Fefferman-Majda, and <br />
Deng-Hou-Yu, to confirm the validity of the singularity. A careful local analysis also <br />
suggests that the blowing-up solution develops a self-similar structure near the point of <br />
the singularity, as the singularity time is approached.<br />
<br />
===Xiaojie Wang(Stony Brook)===<br />
''Uniqueness of Ricci flow solutions on noncompact manifolds''<br />
<br />
Abstract:<br />
Ricci flow is an important evolution equation of Riemannian metrics.<br />
Since it was introduced by R. Hamilton in 1982, it has greatly changed the landscape of riemannian geometry. One of the fundamental question about ricci flow is when is its solution to initial value problem unique. On compact manifold, with arbitrary initial metric, it was confirmed by Hamilton. On noncompact manifold, we only know this is true when further restrictions are imposed to the solution. In this talk, we will discuss various conditions that guarantee the uniqueness. In particular, we will discuss in details with the following uniqueness result. Let $(M,g)$ be a complete noncompact non-collapsing $n$-dimensional riemannian manifold, whose complex sectional curvature is bounded from below and scalar curvature is bounded from above. Then ricci flow with above as its initial data, on $M\times [0,\epsilon]$ for some $\epsilon>0$, has at most one solution in the class of complete riemannian metric with complex sectional curvature bounded from below.<br />
<br />
===Roman Shterenberg(UAB)===<br />
''Recent progress in multidimensional periodic and almost-periodic spectral<br />
problems''<br />
<br />
Abstract: We present a review of the results in multidimensional periodic<br />
and almost-periodic spectral problems. We discuss some recent progress and<br />
old/new ideas used in the constructions. The talk is mostly based on the<br />
joint works with Yu. Karpeshina and L. Parnovski.<br />
<br />
===Antonio Ache(Princeton)===<br />
''Ricci Curvature and the manifold learning problem''<br />
<br />
Abstract: In the first half of this talk we will review several notions of coarse or weak<br />
Ricci Curvature on metric measure spaces which include the works of Lott-Villani, Sturm<br />
and Ollivier. The discussion of the notion of coarse Ricci curvature will serve as <br />
motivation for developing a method to estimate the Ricci curvature of a an embedded<br />
submaifold of Euclidean space from a point cloud which has applications to the Manifold<br />
Learning Problem. Our method is based on combining the notion of ``Carre du Champ"<br />
introduced by Bakry-Emery with a result of Belkin and Niyogi which shows that it is<br />
possible to recover the rough laplacian of embedded submanifolds of the Euclidean space<br />
from point clouds. This is joint work with Micah Warren.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=6073PDE Geometric Analysis seminar2013-10-13T05:29:18Z<p>Zlatos: /* Seminar Schedule Spring 2014 */</p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
<br />
= Seminar Schedule Fall 2013 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Greg Drugan (U. of Washington)<br />
|[[#Greg Drugan (U. of Washington) |<br />
Construction of immersed self-shrinkers]]<br />
|Angenent<br />
|-<br />
|-<br />
|October 7<br />
|[http://users.cms.caltech.edu/~gluo/ Guo Luo (Caltech)]<br />
|[[#Guo Luo (Caltech) |<br />
Potentially Singular Solutions of the 3D Incompressible Euler Equations. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 18<br />
|[http://people.cas.uab.edu/~shterenb/ Roman Shterenberg (UAB)]<br />
|[[#Roman Shterenberg (UAB) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
<br />
= Seminar Schedule Spring 2014 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 14 at 4pm in B139 (TUESDAY), joint with Analysis<br />
|[http://www.math.univ-toulouse.fr/~roque/ Jean-Michel Roquejoffre (Toulouse)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Zlatos<br />
|-<br />
|-<br />
|March 3<br />
|[http://www.dam.brown.edu/people/hdong Hongjie Dong (Brown)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 7<br />
|[http://pi.math.virginia.edu/~zg7c/ Zoran Grujic (University of Virginia)]<br />
|[[#Zoran Grujic (University of Virginia) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
<br />
===Greg Drugan (U. of Washington)===<br />
''Construction of immersed self-shrinkers''<br />
<br />
Abstract: We describe a procedure for constructing immersed<br />
self-shrinking solutions to mean curvature flow. <br />
The self-shrinkers we construct have a rotational symmetry, and<br />
the construction involves a detailed study of geodesics in the<br />
upper-half plane with a conformal metric.<br />
This is a joint work with Stephen Kleene.<br />
<br />
===Guo Luo (Caltech)===<br />
''Potentially Singular Solutions of the 3D Incompressible Euler Equations''<br />
<br />
Abstract:<br />
Whether the 3D incompressible Euler equations can develop a singularity in <br />
finite time from smooth initial data is one of the most challenging problems in <br />
mathematical fluid dynamics. This work attempts to provide an affirmative answer to this <br />
long-standing open question from a numerical point of view, by presenting a class of <br />
potentially singular solutions to the Euler equations computed in axisymmetric <br />
geometries. The solutions satisfy a periodic boundary condition along the axial direction <br />
and no-flow boundary condition on the solid wall. The equations are discretized in space <br />
using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially <br />
designed adaptive (moving) meshes that are dynamically adjusted to the evolving <br />
solutions. With a maximum effective resolution of over $(3 \times 10^{12})^{2}$ near the <br />
point of singularity, we are able to advance the solution up to $\tau_{2} = 0.003505$ and <br />
predict a singularity time of $t_{s} \approx 0.0035056$, while achieving a <br />
\emph{pointwise} relative error of $O(10^{-4})$ in the vorticity vector $\omega$ and <br />
observing a $(3 \times 10^{8})$-fold increase in the maximum vorticity <br />
$\norm{\omega}_{\infty}$. The numerical data is checked against all major blowup <br />
(non-blowup) criteria, including Beale-Kato-Majda, Constantin-Fefferman-Majda, and <br />
Deng-Hou-Yu, to confirm the validity of the singularity. A careful local analysis also <br />
suggests that the blowing-up solution develops a self-similar structure near the point of <br />
the singularity, as the singularity time is approached.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=6072PDE Geometric Analysis seminar2013-10-13T05:28:20Z<p>Zlatos: /* Seminar Schedule Spring 2014 */</p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
<br />
= Seminar Schedule Fall 2013 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Greg Drugan (U. of Washington)<br />
|[[#Greg Drugan (U. of Washington) |<br />
Construction of immersed self-shrinkers]]<br />
|Angenent<br />
|-<br />
|-<br />
|October 7<br />
|[http://users.cms.caltech.edu/~gluo/ Guo Luo (Caltech)]<br />
|[[#Guo Luo (Caltech) |<br />
Potentially Singular Solutions of the 3D Incompressible Euler Equations. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 18<br />
|[http://people.cas.uab.edu/~shterenb/ Roman Shterenberg (UAB)]<br />
|[[#Roman Shterenberg (UAB) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
<br />
= Seminar Schedule Spring 2014 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 14 at 4pm in B139 (TUESDAY, joint with Analysis)<br />
|[http://www.math.univ-toulouse.fr/~roque/ Jean-Michel Roquejoffre (Toulouse)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Zlatos<br />
|-<br />
|-<br />
|March 3<br />
|[http://www.dam.brown.edu/people/hdong Hongjie Dong (Brown)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 7<br />
|[http://pi.math.virginia.edu/~zg7c/ Zoran Grujic (University of Virginia)]<br />
|[[#Zoran Grujic (University of Virginia) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
<br />
===Greg Drugan (U. of Washington)===<br />
''Construction of immersed self-shrinkers''<br />
<br />
Abstract: We describe a procedure for constructing immersed<br />
self-shrinking solutions to mean curvature flow. <br />
The self-shrinkers we construct have a rotational symmetry, and<br />
the construction involves a detailed study of geodesics in the<br />
upper-half plane with a conformal metric.<br />
This is a joint work with Stephen Kleene.<br />
<br />
===Guo Luo (Caltech)===<br />
''Potentially Singular Solutions of the 3D Incompressible Euler Equations''<br />
<br />
Abstract:<br />
Whether the 3D incompressible Euler equations can develop a singularity in <br />
finite time from smooth initial data is one of the most challenging problems in <br />
mathematical fluid dynamics. This work attempts to provide an affirmative answer to this <br />
long-standing open question from a numerical point of view, by presenting a class of <br />
potentially singular solutions to the Euler equations computed in axisymmetric <br />
geometries. The solutions satisfy a periodic boundary condition along the axial direction <br />
and no-flow boundary condition on the solid wall. The equations are discretized in space <br />
using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially <br />
designed adaptive (moving) meshes that are dynamically adjusted to the evolving <br />
solutions. With a maximum effective resolution of over $(3 \times 10^{12})^{2}$ near the <br />
point of singularity, we are able to advance the solution up to $\tau_{2} = 0.003505$ and <br />
predict a singularity time of $t_{s} \approx 0.0035056$, while achieving a <br />
\emph{pointwise} relative error of $O(10^{-4})$ in the vorticity vector $\omega$ and <br />
observing a $(3 \times 10^{8})$-fold increase in the maximum vorticity <br />
$\norm{\omega}_{\infty}$. The numerical data is checked against all major blowup <br />
(non-blowup) criteria, including Beale-Kato-Majda, Constantin-Fefferman-Majda, and <br />
Deng-Hou-Yu, to confirm the validity of the singularity. A careful local analysis also <br />
suggests that the blowing-up solution develops a self-similar structure near the point of <br />
the singularity, as the singularity time is approached.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=6071PDE Geometric Analysis seminar2013-10-13T05:27:15Z<p>Zlatos: /* Seminar Schedule Spring 2014 */</p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
<br />
= Seminar Schedule Fall 2013 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Greg Drugan (U. of Washington)<br />
|[[#Greg Drugan (U. of Washington) |<br />
Construction of immersed self-shrinkers]]<br />
|Angenent<br />
|-<br />
|-<br />
|October 7<br />
|[http://users.cms.caltech.edu/~gluo/ Guo Luo (Caltech)]<br />
|[[#Guo Luo (Caltech) |<br />
Potentially Singular Solutions of the 3D Incompressible Euler Equations. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|November 18<br />
|[http://people.cas.uab.edu/~shterenb/ Roman Shterenberg (UAB)]<br />
|[[#Roman Shterenberg (UAB) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
<br />
= Seminar Schedule Spring 2014 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 14 at 4pm (TUESDAY)<br />
|[http://www.math.univ-toulouse.fr/~roque/ Jean-Michel Roquejoffre (Toulouse)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Zlatos<br />
|-<br />
|-<br />
|March 3<br />
|[http://www.dam.brown.edu/people/hdong Hongjie Dong (Brown)]<br />
|[[#Hongjie Dong (Brown) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|-<br />
|April 7<br />
|[http://pi.math.virginia.edu/~zg7c/ Zoran Grujic (University of Virginia)]<br />
|[[#Zoran Grujic (University of Virginia) |<br />
TBA. ]]<br />
|Kiselev<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
<br />
===Greg Drugan (U. of Washington)===<br />
''Construction of immersed self-shrinkers''<br />
<br />
Abstract: We describe a procedure for constructing immersed<br />
self-shrinking solutions to mean curvature flow. <br />
The self-shrinkers we construct have a rotational symmetry, and<br />
the construction involves a detailed study of geodesics in the<br />
upper-half plane with a conformal metric.<br />
This is a joint work with Stephen Kleene.<br />
<br />
===Guo Luo (Caltech)===<br />
''Potentially Singular Solutions of the 3D Incompressible Euler Equations''<br />
<br />
Abstract:<br />
Whether the 3D incompressible Euler equations can develop a singularity in <br />
finite time from smooth initial data is one of the most challenging problems in <br />
mathematical fluid dynamics. This work attempts to provide an affirmative answer to this <br />
long-standing open question from a numerical point of view, by presenting a class of <br />
potentially singular solutions to the Euler equations computed in axisymmetric <br />
geometries. The solutions satisfy a periodic boundary condition along the axial direction <br />
and no-flow boundary condition on the solid wall. The equations are discretized in space <br />
using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially <br />
designed adaptive (moving) meshes that are dynamically adjusted to the evolving <br />
solutions. With a maximum effective resolution of over $(3 \times 10^{12})^{2}$ near the <br />
point of singularity, we are able to advance the solution up to $\tau_{2} = 0.003505$ and <br />
predict a singularity time of $t_{s} \approx 0.0035056$, while achieving a <br />
\emph{pointwise} relative error of $O(10^{-4})$ in the vorticity vector $\omega$ and <br />
observing a $(3 \times 10^{8})$-fold increase in the maximum vorticity <br />
$\norm{\omega}_{\infty}$. The numerical data is checked against all major blowup <br />
(non-blowup) criteria, including Beale-Kato-Majda, Constantin-Fefferman-Majda, and <br />
Deng-Hou-Yu, to confirm the validity of the singularity. A careful local analysis also <br />
suggests that the blowing-up solution develops a self-similar structure near the point of <br />
the singularity, as the singularity time is approached.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=4383PDE Geometric Analysis seminar2012-09-22T10:08:17Z<p>Zlatos: </p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
= Seminar Schedule Fall 2012 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 17<br />
|[http://www.math.wisc.edu/~bwang/ Bing Wang (UW Madison)]<br />
|[[#Bing Wang (UW Madison)|<br />
On the regularity of limit space]]<br />
|local<br />
|-<br />
|-<br />
|October 15<br />
|[http://www.math.umn.edu/~polacik/ Peter Polacik (University of Minnesota)]<br />
|[[#Peter Polacik (University of Minnesota)|<br />
Exponential separation between positive and sign-changing solutions and its applications]]<br />
|Zlatos<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
===Bing Wang (UW Madison)===<br />
''On the regularity of limit space''<br />
<br />
This is a joint work with Gang Tian. <br />
In this talk, we will discuss how to improve regularity of the limit space by Ricci flow.<br />
We study the structure of the limit space of a sequence of almost Einstein<br />
manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such<br />
manifolds are the initial manifolds of some normalized Ricci flows whose scalar<br />
curvatures are almost constants over space-time in the L1-sense, Ricci curvatures<br />
are bounded from below at the initial time. Under the non-collapsed condition,<br />
we show that the limit space of a sequence of almost Einstein manifolds has most<br />
properties which is known for the limit space of Einstein manifolds. As applications,<br />
we can apply our structure results to study the properties of K¨ahler manifolds.<br />
<br />
<br />
===Peter Polacik (University of Minnesota)===<br />
'' Exponential separation between positive and sign-changing solutions and its applications''<br />
<br />
In linear nonautonomous second-order parabolic equations, the exponential separation refers to the exponential decay of any sign-changing solution relative to any positive solution. In this lecture, after summarizing key results on exponential separation, we show how it can be effectively used in studies of some nonlinear parabolic problems.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=4382PDE Geometric Analysis seminar2012-09-22T10:07:41Z<p>Zlatos: </p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
= Seminar Schedule Fall 2012 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 17<br />
|[http://www.math.wisc.edu/~bwang/ Bing Wang (UW Madison)]<br />
|[[#Bing Wang (UW Madison)|<br />
On the regularity of limit space]]<br />
|local<br />
|-<br />
|-<br />
|October 15<br />
|[http://www.math.umn.edu/~polacik/ Peter Polacik (U of M)]<br />
|[[#Peter Polacik (University of Minnesota)|<br />
Exponential separation between positive and sign-changing solutions and its applications]]<br />
|Zlatos<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
===Bing Wang (UW Madison)===<br />
''On the regularity of limit space''<br />
<br />
This is a joint work with Gang Tian. <br />
In this talk, we will discuss how to improve regularity of the limit space by Ricci flow.<br />
We study the structure of the limit space of a sequence of almost Einstein<br />
manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such<br />
manifolds are the initial manifolds of some normalized Ricci flows whose scalar<br />
curvatures are almost constants over space-time in the L1-sense, Ricci curvatures<br />
are bounded from below at the initial time. Under the non-collapsed condition,<br />
we show that the limit space of a sequence of almost Einstein manifolds has most<br />
properties which is known for the limit space of Einstein manifolds. As applications,<br />
we can apply our structure results to study the properties of K¨ahler manifolds.<br />
<br />
<br />
===Peter Polacik (University of Minnesota)===<br />
'' Exponential separation between positive and sign-changing solutions and its applications''<br />
<br />
In linear nonautonomous second-order parabolic equations, the exponential separation refers to the exponential decay of any sign-changing solution relative to any positive solution. In this lecture, after summarizing key results on exponential separation, we show how it can be effectively used in studies of some nonlinear parabolic problems.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=3974PDE Geometric Analysis seminar2012-07-17T23:04:34Z<p>Zlatos: /* Seminar Schedule Fall 2012 */</p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
= Seminar Schedule Fall 2012 =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|October 15<br />
|[http://www.math.umn.edu/~polacik/ Peter Polacik (U of M)]<br />
|[[#Peter Polacik (U of M)|<br />
To Be Announced]]<br />
|Zlatos<br />
|-<br />
|}<br />
<br />
= Abstracts =<br />
===Peter Polacik (U of M)===<br />
''To Be Announced''<br />
<br />
<Abstract here></div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=Applied_and_Computational_Mathematics&diff=2511Applied and Computational Mathematics2011-09-02T17:04:02Z<p>Zlatos: /* Tenured and tenure-track faculty */</p>
<hr />
<div>__NOTOC__<br />
[[Image:jet.jpg|link=http://www.math.wisc.edu/~jeanluc|frame|jet striking an inclined plane]]<br />
<br />
= '''Applied Mathematics at UW-Madison''' =<br />
<br />
Welcome to the Applied Mathematics Group at the University of Wisconsin, Madison. Our faculty members, postdoctoral fellows, and students are involved in a variety of research projects, including fluid dynamics, partial and stochastic differential equations, scientific computing, biology, biochemistry, and topology.<br />
<br />
<br><br />
<br />
== News and opportunities ==<br />
<br />
* Funding opportunity for a '''graduate student''' to study '''persistence and multistability in biological networks''' (contact [http://www.math.wisc.edu/~craciun Gheorghe Craciun], supported by [http://nih.gov NIH]). <!-- Added by craciun 2011-09-01 --><br />
<br />
* Funding opportunity for a '''graduate student''' to study '''mathematical analysis of mass spectrometry data and proteomics''' (contact [http://www.math.wisc.edu/~craciun Gheorghe Craciun], supported by [http://nsf.gov NSF]). <!-- Added by craciun 2011-09-01 --><br />
<br />
* '''Li Wang''' (PhD student with Leslie Smith) graduated and has a job at [http://www.epic.com/ Epic]. <!-- Added by jeanluc 2011-09-01 --><br />
<br />
* Funding opportunity for a '''graduate student''' to study '''waves in geophysical flows and tropical cyclogenesis''' (contact [http://www.math.wisc.edu/~jeanluc Leslie Smith], supported by [http://nsf.gov NSF]). <!-- Added by jeanluc 2011-09-01 --><br />
<br />
* Funding opportunity for a '''graduate student''' to study '''[http://www.math.wisc.edu/~jeanluc/projsum.pdf mixing by microorganisms]''' (contact [http://www.math.wisc.edu/~jeanluc Jean-Luc Thiffeault], supported by [http://nsf.gov NSF]). <!-- Added by jeanluc 2011-09-01 --><br />
<br />
<br><br />
<br />
== Seminars ==<br />
<br />
''organized by Applied Math''<br />
<br />
* [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied and Computational Math Seminar] (Fridays at 2:25pm, VV 901)<br />
* [http://www.math.wisc.edu/wiki/index.php/Applied/GPS GPS Applied Math Seminar] (Time TBD)<br />
* Joint Math/AOS Informal Seminar (Thursdays at 3:45 pm, AOS 811)<br />
<br />
<br />
''other seminar series of interest''<br />
<br />
* [http://www.math.wisc.edu/wiki/index.php/Colloquia Mathematics Colloquium] (Fridays at 4:00pm, VV B239)<br />
* [http://sprott.physics.wisc.edu/Chaos-Complexity/ Chaos and Complex Systems Seminar] (Tuesdays at 12:05pm, 4274 Chamberlin Hall)<br />
* [http://www.engr.wisc.edu/news/events/index.phtml?start=2011-09-02&range=3650&search=Rheology RRC Lecture] (Fridays at 12:05pm, 1800 Engineering Hall)<br />
* [http://www.physics.wisc.edu/twap/view.php?name=PDC Physics Department Colloquium] (Fridays at 3:30 pm; 2241 Chamberlin Hall)<br />
<br />
<br><br />
<br />
== Tenured and tenure-track faculty ==<br />
<br />
[http://www.math.wisc.edu/~anderson/ David Anderson:] (Duke, 2005) probability and stochastic processes, computational methods for stochastic processes, mathematical/systems biology.<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent:] (Leiden, 1986) partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~assadi/ Amir Assadi:] (Princeton, 1978) computational & mathematical models in molecular biology & neuroscience.<br />
<br />
[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. <br />
<br />
[http://www.math.wisc.edu/~craciun/ Gheorghe Craciun:] (Ohio State, 2002) mathematical biology, biochemical networks, biological interaction networks.<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Representation theory of groups, algebraic geometry, applications to signal Processing, structural biology, mathematical physics.<br />
<br />
[http://www.math.wisc.edu/~jin/ Shi Jin:] (Arizona, 1991) applied & computational mathematics.<br />
<br />
[http://www.math.wisc.edu/~kiselev/ Alex (Sasha) Kiselev:] (CalTech, 1997) partial differential equations, Fourier analysis<br />
and applications in fluid mechanics, combustion, mathematical biology and Schr&ouml;dinger operators.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa:] (Minnesota, 1991) differential geometry, applied math.<br />
<br />
[http://www.math.wisc.edu/~milewski/ Paul Milewski:] (MIT, 1993) applied mathematics, fluid dynamics.<br />
<br />
[http://www.math.wisc.edu/~mitchell/ Julie Mitchell:] (Berkeley, 1998) computational mathematics, structural biology.<br />
<br />
[http://www.math.wisc.edu/~rossmani/ James Rossmanith:] (Washington, 2002) computational mathematics, hyperbolic conservation laws, plasma physics.<br />
<br />
[http://www.math.wisc.edu/~lsmith/ Leslie Smith:] (MIT, 1988) applied mathematics. Waves and coherent structures in oceanic and atmospheric flows. <br />
<br />
[http://www.math.wisc.edu/~stech/ Sam Stechmann:] (Courant, 2008) fluid dynamics, atmospheric science, computational mathematics.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault:] (Texas, 1998) fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
[http://www.math.wisc.edu/~waleffe/ Fabian Waleffe:] (MIT, 1989) applied and computational mathematics. Fluid dynamics, hydrodynamic instabilities. Turbulence and unstable coherent flows.<br />
<br />
[http://www.math.wisc.edu/~zlatos/ Andrej Zlatos:] (Caltech, 2003) partial differential equations, combustion, fluid dynamics, Schrödinger operators, orthogonal polynomials<br />
<br />
<br><br />
<br />
== Postdoctoral fellows ==<br />
<br />
<!-- [http://www.math.wisc.edu/~dwei/ Dongming Wei:] (Maryland, 2007) nonlinear partial differential equations, applied analysis, and numerical computation. --><br />
<br />
[http://www.math.wisc.edu/~hernande Gerardo Hernandez-Duenas:] (Michigan, 2011)<br />
<br />
<br><br />
<br />
== Current Graduate Students ==<br />
<br />
Adel Ardalan: Student of Amir Assadi.<br />
<br />
Daniela Banu: Student of Paul Milewski.<br />
<br />
[http://www.math.wisc.edu/~bookasam/ Anekewit (Tete) Boonkasame:] Student of Paul Milewski.<br />
<br />
Yongtao Cheng: Student of James Rossmanith.<br />
<br />
[http://vv811a.math.wisc.edu/index.html/index.php/component/content/article/40 Hesam Dashti:] Student of Amir Assadi.<br />
<br />
[http://www.math.wisc.edu/~qdeng/ Qiang Deng:] Student of Leslie Smith.<br />
<br />
[http://vv811a.math.wisc.edu/index.html/index.php/component/content/article/33 Alireza Fotuhi:] Student of Amir Assadi.<br />
<br />
[http://www.math.wisc.edu/~jefferis/ Leland Jefferis:] Student of Shi Jin.<br />
<br />
[http://www.math.wisc.edu/~ejohnson/ E. Alec Johnson:] Student of James Rossmanith.<br />
<br />
[http://vv811a.math.wisc.edu/index.html/index.php/component/content/article/15 Mohammad Khabbazian:] Student of Amir Assadi.<br />
<br />
[http://www.math.wisc.edu/~koyama/ Masanori (Maso) Koyama:] Student of David Anderson.<br />
<br />
[http://www.math.wisc.edu/~leili/ Lei Li:] Student of Shi Jin.<br />
<br />
[http://www.math.wisc.edu/~qinli/ Qin Li:] Student of Shi Jin.<br />
<br />
[http://www.math.wisc.edu/~pqi/ Peng Qi:] Student of Shi Jin.<br />
<br />
[http://vv811a.math.wisc.edu/index.html/index.php/component/content/article/16 Arash Sangari:] Student of Amir Assadi.<br />
<br />
[http://www.math.wisc.edu/~seal/ David Seal:] Student of James Rossmanith.<br />
<br />
Ebru Selin Selen: Student of Amir Assadi.<br />
<br />
[http://www.math.wisc.edu/~matz/ Sarah Tumasz:] Student of Jean-Luc Thiffeault.<br />
<br />
Li Wang: Student of Leslie Smith.<br />
<br />
[http://www.math.wisc.edu/~wangli/ Li (Aug) Wang:] Student of Shi Jin.<br />
<br />
[http://www.math.wisc.edu/~yan/ Bokai Yan:] Student of Shi Jin.<br />
<br />
Qian You: Student of Sigurd Angenent.<br />
<br />
[http://www.math.wisc.edu/~zhou/ Zhennan Zhou:] Student of Shi Jin.<br />
<br />
<!-- Past students: --><br />
<!-- [http://www.math.wisc.edu/~hu/ Jingwei Hu:] Student of Shi Jin. --><br />
<br />
<br><br />
<br />
== Graduate course offerings ==<br />
<br />
=== Fall 2011 ===<br />
<br />
* Math 605: [http://www.math.wisc.edu/math-727-calculus-variations-0 Stochastic Methods for Biology] (D. Anderson)<br />
* Math 703: [http://www.math.wisc.edu/math-703-methods-applied-mathematics-i Methods of Applied Mathematics II] (L. Smith)<br />
* Math 707: [http://www.math.wisc.edu/math707-ema700-theory-elasticity Theory of Elasticity] (F. Waleffe)<br />
* Math 714: [http://www.math.wisc.edu/math-714-scientific-computing Methods of Computational Math I] (J. Mitchell)<br />
* Math 801: [http://www.math.wisc.edu/801-waves-fluids Comp Math Applied to Biology] (A. Assadi)<br />
* Math 837: [http://www.math.wisc.edu/math-837-topics-numerical-analysis Topics in Numerical Analysis] (S. Jin)<br />
<br />
<!--<br />
Spring 2011:<br />
* Math 609: [https://www.math.wisc.edu/609-mathematical-methods-systems-biology Mathematical Methods for Systems Biology] (G. Craciun)<br />
* Math 704: [https://www.math.wisc.edu/704-methods-applied-mathematics-2 Methods of Applied Mathematics II] (S. Stechmann)<br />
* Math/CS 715: [https://www.math.wisc.edu/715-methods-computational-math-ii Methods of Computational Math II] (S. Jin)<br />
* Math 801: [https://www.math.wisc.edu/math-801-hydrodynamic-instabilities-chaos-and-turbulence Hydrodynamic Instabilities, Chaos and Turbulence] (F. Waleffe)<br />
* Math 826: [https://www.math.wisc.edu/826-Functional-Analysis Partial Differential Equations in Fluids and Biology] (A. Kiselev)<br />
* Math/CS 837: [https://www.math.wisc.edu/837-Numerical-Analysis Numerical Methods for Hyperbolic PDEs] (J. Rossmanith)<br />
--><br />
<br />
<br><br />
<br />
----<br />
Return to the [http://www.math.wisc.edu/wiki/index.php Mathematics Department Wiki Page]</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1903PDE Geometric Analysis seminar2011-04-04T19:25:11Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''Optimization of eigenvalues of non-symmetric elliptic operators'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''Symmetry properties of parabolic problems and their applications'']]<br />
|Zlatos<br />
|-<br />
|Apr 11<br />
|Alexey Cheskidov (UIC)<br />
|[[#Alexey Cheskidov (UIC)|<br />
''Navier-Stokes and Euler equations: a unified approach to the problem of blow-up'']]<br />
|Kiselev<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.<br />
<br />
===Francois Hamel (Marseille)===<br />
''Optimization of eigenvalues of non-symmetric elliptic operators''<br />
<br />
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of <math>R^n</math>. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.<br />
<br />
===Juraj Foldes (Vanderbilt)===<br />
''Symmetry properties of parabolic problems and their applications''<br />
<br />
Positive solutions of nonlinear parabolic problems can have a very complex behavior. However, assuming certain symmetry conditions, it is possible to prove that the solutions converge to the space of symmetric functions. We show that this property is 'stable'; more specifically if the symmetry conditions are replaced by asymptotically symmetric ones, the solutions still approach the space of symmetric functions. As an application, we show new results on convergence of solutions to a single equilibrium.<br />
<br />
===Alexey Cheskidov (UIC)===<br />
''Navier-Stokes and Euler equations: a unified approach to the problem of blow-up''<br />
<br />
The problems of blow-up for Navier-Stokes and Euler equations <br />
have been extensively studied for decades using different techniques. <br />
Motivated by Kolmogorov's theory of turbulence, we present a new unified <br />
approach to the blow-up problem for the equations of incompressible <br />
fluid motion. In particular, we present a new regularity criterion which <br />
is weaker than the Beale-Kato-Majda condition in the inviscid case, and <br />
weaker than every Ladyzhenskaya-Prodi-Serrin condition in the viscous case.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1880PDE Geometric Analysis seminar2011-03-24T16:33:10Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''Optimization of eigenvalues of non-symmetric elliptic operators'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''Symmetry properties of parabolic problems and their applications'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.<br />
<br />
===Francois Hamel (Marseille)===<br />
''Optimization of eigenvalues of non-symmetric elliptic operators''<br />
<br />
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of <math>R^n</math>. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.<br />
<br />
===Juraj Foldes (Vanderbilt)===<br />
''Symmetry properties of parabolic problems and their applications''<br />
<br />
Positive solutions of nonlinear parabolic problems can have a very complex behavior. However, assuming certain symmetry conditions, it is possible to prove that the solutions converge to the space of symmetric functions. We show that this property is 'stable'; more specifically if the symmetry conditions are replaced by asymptotically symmetric ones, the solutions still approach the space of symmetric functions. As an application, we show new results on convergence of solutions to a single equilibrium.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1840PDE Geometric Analysis seminar2011-03-10T05:08:40Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''Optimization of eigenvalues of non-symmetric elliptic operators'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.<br />
<br />
===Francois Hamel (Marseille)===<br />
''Optimization of eigenvalues of non-symmetric elliptic operators''<br />
<br />
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of <math>R^n</math>. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1839PDE Geometric Analysis seminar2011-03-10T05:08:15Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 15 at 4pm in B139 (joint wit Analysis)<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''Optimization of eigenvalues of non-symmetric elliptic operators'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.<br />
<br />
===Francois Hamel (Marseille)===<br />
''Optimization of eigenvalues of non-symmetric elliptic operators''<br />
<br />
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of <math>R^n</math>. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1696PDE Geometric Analysis seminar2011-02-13T02:49:51Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 14<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''Optimization of eigenvalues of non-symmetric elliptic operators'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.<br />
<br />
===Francois Hamel (Marseille)===<br />
''Optimization of eigenvalues of non-symmetric elliptic operators''<br />
<br />
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of <math>R^n</math>. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1695PDE Geometric Analysis seminar2011-02-13T02:49:13Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 14<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.<br />
<br />
===Francois Hamel (Marseille)===<br />
''Optimization of eigenvalues of non-symmetric elliptic operators''<br />
<br />
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of <math>R^n</math>. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1560PDE Geometric Analysis seminar2011-01-29T14:54:12Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 14<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1559PDE Geometric Analysis seminar2011-01-29T14:53:59Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 28<br />
|Francois Hamel (Marseille)<br />
|[[#Francois Hamel (Marseille)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.</div>Zlatoshttps://wiki.math.wisc.edu/index.php?title=PDE_Geometric_Analysis_seminar&diff=1463PDE Geometric Analysis seminar2011-01-19T22:35:51Z<p>Zlatos: </p>
<hr />
<div>= PDE and Geometric Analysis Seminar =<br />
<br />
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
== Seminar Schedule Spring 2011 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|Bing Wang (Princeton)<br />
|[[#Bing Wang (Princeton)|<br />
''The Kaehler Ricci flow on Fano manifold '']]<br />
|Viaclovsky<br />
|-<br />
|Mar 28<br />
|Juraj Foldes (Vanderbilt)<br />
|[[#Juraj Foldes (Vanderbilt)|<br />
''TBA'']]<br />
|Zlatos<br />
|-<br />
|Date TBA<br />
|Mikhail Feldman (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|Date TBA<br />
|Sigurd Angenent (UW Madison)<br />
|''TBA''<br />
|Local speaker<br />
|-<br />
|}<br />
== Seminar Schedule Fall 2010 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 13<br />
|Fausto Ferrari (Bologna)<br />
|[[#Fausto Ferrari (Bologna)|<br />
''Semilinear PDEs and some symmetry properties of stable solutions'']]<br />
|Feldman<br />
|-<br />
|Sept 27<br />
|Arshak Petrosyan (Purdue)<br />
|[[#Arshak Petrosyan (Purdue)|<br />
''Nonuniqueness in a free boundary problem from combustion'']]<br />
|Feldman<br />
|-<br />
|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Changyou Wang (U. of Kentucky)<br />
|[[#Changyou Wang (U. of Kentucky)|<br />
''Phase transition for higher dimensional wells'']]<br />
|Feldman<br />
|-<br />
|Oct 11<br />
|Philippe LeFloch (Paris VI)<br />
|[[#Philippe LeFloch (Paris VI)|<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries'']]<br />
|Feldman<br />
|-<br />
|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. '''Special day, time & room.'''<br />
|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)<br />
|[[#Irina Mitrea |<br />
''Boundary Value Problems for Higher Order Differential Operators'']]<br />
|[https://www.math.wisc.edu/~wimaw/ WiMaW]<br />
|-<br />
|-<br />
|Nov 1<br />
|Panagiota Daskalopoulos (Columbia U)<br />
|[[#Panagiota Daskalopoulos (Columbia U)|<br />
''Ancient solutions to geometric flows'']]<br />
|Feldman<br />
|-<br />
|Nov 8<br />
|Maria Gualdani (UT Austin)<br />
|[[#Maria Gualdani (UT Austin)|<br />
''A nonlinear diffusion model in mean-field games'']]<br />
|Feldman<br />
|-<br />
|Nov 18 Thursday 1:20pm Room: 901 Van Vleck '''Special day & time.'''<br />
|Hiroshi Matano (Tokyo University) <br />
|[[#Hiroshi Matano (Tokyo University)|<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit'']]<br />
|Angenent & Rabinowitz<br />
|-<br />
|Nov 29<br />
|Ian Tice (Brown University)<br />
|[[#Ian Tice (Brown University)|<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension'']]<br />
|Feldman<br />
|-<br />
|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. '''Special day, time & room.'''<br />
|Hoai Minh Nguyen (NYU-Courant Institute)<br />
|[[#Hoai Minh Nguyen (NYU-Courant Institute)|<br />
''Cloaking via change of variables for the Helmholtz equation'']]<br />
|Feldman<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Fausto Ferrari (Bologna)===<br />
''Semilinear PDEs and some symmetry properties of stable solutions''<br />
<br />
I will deal with stable solutions of semilinear elliptic PDE's <br />
and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.<br />
<br />
===Arshak Petrosyan (Purdue)===<br />
''Nonuniqueness in a free boundary problem from combustion''<br />
<br />
We consider a parabolic free boundary problem with a fixed gradient condition<br />
which serves as a simplified model for the propagation of premixed equidiffusional<br />
flames. We give a rigorous justification of an example due to J.L. V ́azquez that <br />
the initial data in the form of two circular humps leads to the nonuniqueness of limit <br />
solutions if the supports of the humps touch at the time of their maximal expansion.<br />
<br />
This is a joint work with Aaron Yip.<br />
<br />
<br />
===Changyou Wang (U. of Kentucky)===<br />
''Phase transition for higher dimensional wells''<br />
<br />
For a potential function <math>F</math> that has two global minimum sets consisting of two compact connected<br />
Riemannian submanifolds in <math style="vertical-align=100%" >\mathbb{R}^k</math>, we consider the singular perturbation problem:<br />
<br />
Minimizing <math>\int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right)</math> under given Dirichlet boundary data.<br />
<br />
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter <math>\epsilon</math><br />
tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and<br />
the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary<br />
data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.<br />
<br />
===Philippe LeFloch (Paris VI)===<br />
''Kinetic relations for undercompressive shock waves and propagating phase boundaries''<br />
<br />
I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves. <br />
<br />
<br />
<br />
===Irina Mitrea===<br />
''Boundary Value Problems for Higher Order Differential Operators''<br />
<br />
As is well known, many phenomena in engineering and mathematical physics<br />
can be modeled by means of boundary value problems for a certain elliptic<br />
differential operator L in a domain D.<br />
<br />
When L is a differential operator of second order a variety of tools<br />
are available for dealing with such problems including boundary integral<br />
methods,<br />
variational methods, harmonic measure techniques, and methods based on<br />
classical<br />
harmonic analysis. The situation when the differential operator has higher order<br />
(as is the case for instance with anisotropic plate bending when one<br />
deals with<br />
fourth order) stands in sharp contrast with this as only fewer options<br />
could be<br />
successfully implemented. Alberto Calderon, one of the founders of the<br />
modern theory<br />
of Singular Integral Operators, has advocated in the seventies the use<br />
of layer potentials<br />
for the treatment of higher order elliptic boundary value problems.<br />
While the<br />
layer potential method has proved to be tremendously successful in the<br />
treatment<br />
of second order problems, this approach is insufficiently developed to deal<br />
with the intricacies of the theory of higher order operators. In fact,<br />
it is largely<br />
absent from the literature dealing with such problems.<br />
<br />
In this talk I will discuss recent progress in developing a multiple<br />
layer potential<br />
approach for the treatment of boundary value problems associated with<br />
higher order elliptic differential operators. This is done in a very<br />
general class<br />
of domains which is in the nature of best possible from the point of<br />
view of<br />
geometric measure theory. <br />
<br />
<br />
===Panagiota Daskalopoulos (Columbia U)===<br />
''Ancient solutions to geometric flows''<br />
<br />
We will discuss the clasification of ancient solutions to nonlinear geometric flows. <br />
It is well known that ancient solutions appear as blow up limits at a finite time <br />
singularity of the flow.<br />
Special emphasis will be given to the 2-dimensional Ricci flow.<br />
In this case we will show that ancient compact solution<br />
is either the Einstein (trivial) or one of the King-Rosenau solutions. <br />
<br />
===Maria Gualdani (UT Austin)===<br />
''A nonlinear diffusion model in mean-field games''<br />
<br />
We present an overview of mean-field games theory and show <br />
recent results on a free boundary value problem, which models <br />
price formation dynamics. <br />
In such model, the price is formed through a game among infinite number <br />
of agents. <br />
Existence and regularity results, as well as linear stability, will be shown.<br />
<br />
===Hiroshi Matano (Tokyo University)===<br />
''Traveling waves in a sawtoothed cylinder and their homogenization limit''<br />
<br />
My talk is concerned with a curvature-dependent motion of plane <br />
curves in a two-dimensional cylinder with spatially undulating<br />
boundary. In other words, the boundary has many bumps and we <br />
assume that the bumps are aligned in a spatially recurrent manner.<br />
<br />
The goal is to study how the average speed of the traveling wave <br />
depends on the geometry of the domain boundary. More specifically, <br />
we consider the homogenization problem as the boundary undulation <br />
becomes finer and finer, and determine the homogenization limit <br />
of the average speed and the limit profile of the traveling waves. <br />
Quite surprisingly, this homogenized speed depends only on the <br />
maximal opening angles of the domain boundary and no other <br />
geometrical features are relevant. <br />
<br />
Next we consider the special case where the boundary undulation <br />
is quasi-periodic with ''m'' independent frequencies. We show that <br />
the rate of convergence to the homogenization limit depends on<br />
this number ''m''.<br />
<br />
This is joint work with Bendong Lou and Ken-Ichi Nakamura.<br />
<br />
===Ian Tice (Brown University)===<br />
''Global well-posedness and decay for the viscous surface wave<br />
problem without surface tension''<br />
<br />
We study the incompressible, gravity-driven Navier-Stokes<br />
equations in three dimensional domains with free upper boundaries and<br />
fixed lower boundaries, in both the horizontally periodic and<br />
non-periodic settings. The effect of surface tension is not included.<br />
We employ a novel two-tier nonlinear energy method that couples the<br />
boundedness of certain high-regularity norms to the algebraic decay of<br />
lower-regularity norms. The algebraic decay allows us to balance the<br />
growth of the highest order derivatives of the free surface function,<br />
which then allows us to derive a priori estimates for solutions. We<br />
then prove local well-posedness in our energy space, which yields global<br />
well-posedness and decay. The novel LWP theory is established through<br />
the study of the linear Stokes problem in moving domains. This is joint<br />
work with Yan Guo.<br />
<br />
<br />
===Hoai Minh Nguyen (NYU-Courant Institute)===<br />
''Cloaking via change of variables for the Helmholtz equation''<br />
<br />
A region of space is cloaked for a class of measurements if observers<br />
are not only unaware of its contents, but also unaware of the presence<br />
of the cloak using such measurements. One approach to cloaking is the<br />
change of variables scheme introduced by Greenleaf, Lassas, and<br />
Uhlmann for electrical impedance tomography and by Pendry, Schurig,<br />
and Smith for the Maxwell equation. They used a singular change of<br />
variables which blows up a point into the cloaked region. To avoid<br />
this singularity, various regularized schemes have been proposed. In<br />
this talk I present results related to cloaking via change of<br />
variables for the Helmholtz equation using the natural regularized<br />
scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the<br />
authors used a transformation which blows up a small ball instead of a<br />
point into the cloaked region. I will discuss the degree of<br />
invisibility for a finite range or the full range of frequencies, and<br />
the possibility of achieving perfect cloaking. If time permits, I will<br />
mention some results related to the wave equation.<br />
<br />
===Bing Wang (Princeton)===<br />
''The Kaehler Ricci flow on Fano manifold ''<br />
<br />
We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big <math>\alpha_{\nu, 1}</math><br />
or <math>\alpha_{\nu, 2}</math> (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds.<br />
Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics<br />
on orbifolds by calculating Tian's invariants.<br />
An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.</div>Zlatos