Difference between revisions of "PDE Geometric Analysis seminar"

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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Spring 2016 | Tentative schedule for Spring 2016]]===
+
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
  
  
= Seminar Schedule Fall 2015 =
+
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==
{| cellpadding="8"
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Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. 
!align="left" | date 
+
 
!align="left" | speaker
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'''Week 1 (9/1/2020-9/5/2020)'''
!align="left" | title
+
 
!align="left" | host(s)
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1. Paul Rabinowitz - The calculus of variations and phase transition problems.
|-
+

https://www.youtube.com/watch?v=vs3rd8RPosA
|September 7 (Labor Day)
+
 
|
+
2. Frank Merle - On the implosion of a three dimensional compressible fluid.
|[[#  |  ]]
+
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 
|
+
 
|-
+
'''Week 2 (9/6/2020-9/12/2020)'''
|September 14 (special room: B115)
+
 
| Hung Tran (Madison)
+
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.
|[[#Hung Tran  | Some inverse problems in periodic homogenization of Hamilton--Jacobi equations ]]
+
https://www.youtube.com/watch?v=4ndtUh38AU0
|
+
 
|-  
+
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI
|September 21 (special room: B115)
+
 
| Eric Baer (Madison)
+
 
||[[#Eric Baer | Optimal function spaces for continuity of the Hessian determinant as a distribution ]]
+
 
+
'''Week 3 (9/13/2020-9/19/2020)'''
|-
+
 
|September 28
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1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
| Donghyun Lee (Madison)
+
 
|[[#Donghyun Lee  | FLUIDS WITH FREE-SURFACE AND VANISHING VISCOSITY LIMIT]]
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2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
+
 
|-
+
 
|October 5
+
 
|Hyung-Ju Hwang (Postech & Brown Univ)
+
'''Week 4 (9/20/2020-9/26/2020)'''
|[[#Hyung-Ju Hwang | The Fokker-Planck equation in bounded domains  ]]
+
 
| Kim
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1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be
|-
 
|October 12
 
| Minh Binh Tran (Madison)
 
|[[#Minh Binh Tran | Nonlinear approximation theory for kinetic equations ]]
 
|
 
|-
 
|October 19
 
| Bob Jensen (Loyola University Chicago)
 
||[[# Bob Jensen | TBA ]]
 
| Tran
 
|-
 
|October 26
 
|Luis Silvestre (Chicago)
 
|[[# Luis Silvestre  | TBA  ]]
 
|Kim
 
|-
 
|November 2
 
| Connor Mooney (UT Austin)
 
|[[# Connor Mooney | TBA  ]]
 
|Lin
 
|-
 
|November 9
 
| Javier Gomez-Serrano (Princeton)
 
||[[# Javier Gomez-Serrano | TBA  ]]
 
|Zlatos
 
|-
 
|November 16
 
| Yifeng Yu (UC Irvine)
 
|[[# Yifeng Yu | TBA ]]
 
| Tran
 
|-
 
|November 23
 
| Nam Le (Indiana)
 
|[[# Nam Le | TBA ]]
 
|Tran
 
|-
 
|November 30
 
| Qin Li (Madison)
 
|[[# Qin Li | TBA ]]
 
|
 
|-
 
|December 7
 
| Lu Wang (Madison)
 
||[[# Lu Wang | TBA  ]]
 
|
 
|-
 
|December 14
 
| Christophe Lacave (Paris 7)
 
|[[# Christophe Lacave | TBA ]]
 
| Zlatos
 
|}
 
  
=Abstract=
+
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM
  
===Hung Tran===
 
  
Some inverse problems in periodic homogenization of Hamilton--Jacobi equations.
 
  
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.
+
'''Week 5 (9/27/2020-10/03/2020)'''
  
 +
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo
  
===Eric Baer===
+
2.  Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c
  
Optimal function spaces for continuity of the Hessian determinant as a distribution.
 
  
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.
+
'''Week 6 (10/04/2020-10/10/2020)'''
  
===Donghyun Lee===
+
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=3
  
FLUIDS WITH FREE-SURFACE AND VANISHING VISCOSITY LIMIT.
+
2.  
  
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.
 
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.
 
  
=== Hyung Ju Hwang===
 
  
The Fokker-Planck equation in bounded domains
+
{| cellpadding="8"
 +
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|-  
 +
|}
  
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.
+
== Abstracts ==
  
=== Minh Binh Tran ===
+
=== ===
  
Nonlinear approximation theory for kinetic equations
+
Title: 
  
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
+
Abstract:
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.
 

Latest revision as of 10:26, 29 September 2020

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Previous PDE/GA seminars

Tentative schedule for Fall 2021-Spring 2022

PDE GA Seminar Schedule Fall 2020-Spring 2021

Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. 

Week 1 (9/1/2020-9/5/2020)

1. Paul Rabinowitz - The calculus of variations and phase transition problems. 
https://www.youtube.com/watch?v=vs3rd8RPosA

2. Frank Merle - On the implosion of a three dimensional compressible fluid. https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 

Week 2 (9/6/2020-9/12/2020)

1. Yoshikazu Giga - On large time behavior of growth by birth and spread. https://www.youtube.com/watch?v=4ndtUh38AU0

2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI


Week 3 (9/13/2020-9/19/2020)

1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ

2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE


Week 4 (9/20/2020-9/26/2020)

1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be

2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM


Week 5 (9/27/2020-10/03/2020)

1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo

2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c


Week 6 (10/04/2020-10/10/2020)

1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=3

2.


date speaker title host(s)

Abstracts

Title:

Abstract: