Difference between revisions of "PDE Geometric Analysis seminar"

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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===
+
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==
 
  
  
{| cellpadding="8"
+
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==
!style="width:20%" align="left" | date 
+
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" | speaker
+
 
!align="left" | title
+
'''Week 1 (9/1/2020-9/5/2020)'''
!style="width:20%" align="left" | host(s)
+
 
|-
+
1. Paul Rabinowitz - The calculus of variations and phase transition problems.
|Sep 9
+

https://www.youtube.com/watch?v=vs3rd8RPosA
| Scott Smith (UW Madison)
+
 
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]
+
2. Frank Merle - On the implosion of a three dimensional compressible fluid.
| Kim and Tran
+
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 
|-
+
 
|Sep 14-15
+
'''Week 2 (9/6/2020-9/12/2020)'''
|
+
 
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html  ]]
+
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.
+
https://www.youtube.com/watch?v=4ndtUh38AU0
|- 
+
 
|Sep 23
+
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI
| Son Tu (UW Madison)
+
 
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]
+
 
| Kim and Tran
+
 
|- 
+
'''Week 3 (9/13/2020-9/19/2020)'''
|Sep 28-29, VV901
+
 
https://www.ki-net.umd.edu/content/conf?event_id=993
+
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
|  |  Recent progress in analytical aspects of kinetic equations and related fluid models 
+
 
+
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
|- 
+
 
|Oct 7
+
 
| Jin Woo Jang (Postech)
+
 
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]
+
'''Week 4 (9/20/2020-9/26/2020)'''
| Kim
+
 
|-
+
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
|Oct 14
+
 
| Stefania Patrizi (UT Austin)
+
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]
+
 
| Tran
+
 
|- 
+
 
|Oct 21
+
'''Week 5 (9/27/2020-10/03/2020)'''
| Claude Bardos (Université Paris Denis Diderot, France)
+
 
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]
+
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo
| Li
+
 
|-  
+
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c
|Oct 25-27, VV901
+
 
| https://www.ki-net.umd.edu/content/conf?event_id=1015
+
 
||  Forward and Inverse Problems in Kinetic Theory
+
'''Week 6 (10/04/2020-10/10/2020)'''
| Li
+
 
|-  
+
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
|Oct 28
+
 
| Albert Ai (UW Madison)
+
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates  ]]
+
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html
| Ifrim
+
 
|-
+
 
|Nov 4
+
'''Week 7 (10/11/2020-10/17/2020)'''
| Yunbai Cao (UW Madison)
+
 
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]
+
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s
| Kim and Tran
+
 
|- 
+
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg
|Nov 18
+
 
| Ilyas Khan (UW Madison)
+
 
|[[#Ilyas Khan | TBA ]]
+
'''Week 8 (10/18/2020-10/24/2020)'''
| Kim and Tran
+
 
|-
+
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg
|Nov 25
+
 
| Mathew Langford (UT Knoxville)
+
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ
|[[#Speaker | TBA ]]
+
 
| Angenent
+
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.
|-
+
 
|-
+
 
|Feb 17
+
'''Week 9 (10/25/2020-10/31/2020)'''
| Yannick Sire (JHU)
+
 
|[[#Yannick Sire (JHU) | TBA ]]
+
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE
| Tran
+
 
|-
+
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764
|Feb 24
+
 
| Matthew Schrecker (UW Madison)
+
 
|[[#Matthew Schrecker | TBA ]]
+
 
| Feldman
+
'''Week 10 (11/1/2020-11/7/2020)'''
|-
+
 
|March 2
+
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be
| Theodora Bourni (UT Knoxville)
+
 
|[[#Speaker | TBA ]]
+
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html
| Angenent
+
 
|- 
+
 
|March 9
+
 
| Ian Tice (CMU)
+
'''Week 11 (11/8/2020-11/14/2020)'''
|[[#Ian Tice| TBA ]]
 
| Kim
 
|-
 
|March 16
 
| No seminar (spring break)
 
|[[#Speaker | TBA ]]
 
| Host
 
|- 
 
|March 23
 
| Jared Speck (Vanderbilt)
 
|[[#Jared Speck | TBA ]]
 
| SCHRECKER
 
|-
 
|March 30
 
| Huy Nguyen (Brown)
 
|[[#Huy Nguyen | TBA ]]
 
| organizer
 
|-
 
|April 6
 
| Speaker (Institute)
 
|[[#Speaker | TBA ]]
 
| Host
 
|-
 
|April 13
 
| Speaker (Institute)
 
|[[#Speaker | TBA ]]
 
| Host
 
|-
 
|April 20
 
| Hyunju Kwon (IAS)
 
|[[#Hyunju Kwon | TBA ]]
 
| Kim
 
|- 
 
|April 27
 
| Speaker (Institute)
 
|[[#Speaker | TBA ]]
 
| Host
 
|-
 
|May 18-21
 
| Madison Workshop in PDE 2020
 
|[[#Speaker | TBA ]]
 
| Tran
 
|}
 
  
== Abstracts ==
+
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc
  
===Scott Smith===
+
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0
  
Title: Recent progress on singular, quasi-linear stochastic PDE
 
  
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing .  These equations are ill-posed in the traditional sense of distribution theory.  They require flexibility in the notion of solution as well as new a priori bounds.  Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory.  This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.
+
'''Week 12 (11/15/2020-11/21/2020)'''
  
 +
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY
  
===Son Tu===
+
2.  Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk
  
Title: State-Constraint static Hamilton-Jacobi equations in nested domains
 
  
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases,  the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).
+
'''Week 13 (11/22/2020-11/28/2020)'''
  
 +
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be
  
===Jin Woo Jang===
+
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8
  
Title: On a Cauchy problem for the Landau-Boltzmann equation
+
'''Week 14 (11/29/2020-12/5/2020)'''
  
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.
+
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations,  
 +
https://youtu.be/xfAKGc0IEUw
  
 +
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc
  
===Stefania Patrizi===
 
  
Title:
 
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity
 
  
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic  limit of  solutions of  Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is  joint work with E. Valdinoci.
+
'''Week 15 (12/6/2020-12/12/2020)'''
  
 +
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be
  
===Claude Bardos===
 
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture
 
  
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.
+
{| cellpadding="8"
 +
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|- 
 +
|}
  
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.
+
== Abstracts ==
  
Eventually the above results are compared with several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.
+
=== ===
  
===Albert Ai===
+
Title:
Title: Two dimensional gravity waves at low regularity: Energy estimates
 
  
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.
+
Abstract:

Latest revision as of 18:53, 29 November 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

2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html


Week 7 (10/11/2020-10/17/2020)

1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s

2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg


Week 8 (10/18/2020-10/24/2020)

1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg

2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ

Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.


Week 9 (10/25/2020-10/31/2020)

1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE

2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764


Week 10 (11/1/2020-11/7/2020)

1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be

2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html


Week 11 (11/8/2020-11/14/2020)

1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc

2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0


Week 12 (11/15/2020-11/21/2020)

1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY

2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk


Week 13 (11/22/2020-11/28/2020)

1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be

2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8

Week 14 (11/29/2020-12/5/2020)

1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, https://youtu.be/xfAKGc0IEUw

2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc


Week 15 (12/6/2020-12/12/2020)

1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be


date speaker title host(s)

Abstracts

Title:

Abstract: