Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2020-Spring 2021)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2015 | Tentative schedule for Fall 2015]]===
+
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
= Seminar Schedule Spring 2015 =
 
{| cellpadding="8"
 
!align="left" | date 
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | host(s)
 
|-
 
|January 21 (Departmental Colloquium: 4PM, B239)
 
|Jun Kitagawa (Toronto) 
 
|[[#Jun Kitagawa (Toronto)  | Regularity theory for generated Jacobian equations: from optimal transport to geometric optics  ]]
 
|Feldman
 
|-
 
|February 9
 
|Jessica Lin (Madison)
 
|[[#Jessica Lin (Madison)  | Algebraic Error Estimates for the Stochastic Homogenization of Uniformly Parabolic Equations ]]
 
|Kim
 
|-
 
|February 16
 
|
 
|[[#  |  ]]
 
|
 
|-
 
|February 17 (joint with Analysis Seminar: 4PM, B139)
 
|Chanwoo Kim (Madison)
 
|[[#Chanwoo Kim (Madison)  | Hydrodynamic limit from the Boltzmann to the Navier-Stokes-Fourier ]]
 
|Seeger
 
|-
 
|February 23
 
|Jennifer Beichman (Madison) 
 
|[[#Jennifer Beichman (Madison)  | TBA ]]
 
| Kim
 
|-
 
|March 2
 
|Benoit Pausader (Princeton)
 
|[[#Benoit Pausader (Princeton) | TBA]]
 
|Kim
 
|-
 
|March 9
 
|Haozhao Li (University of Science and Technology of China)
 
|[[#Haozhao Li|Regularity scales and convergence of the Calabi flow]]
 
|Wang
 
|-
 
|March 16
 
|
 
|[[#  |  ]]
 
|
 
|-
 
|March 23
 
| Ben Fehrman (University of Chicago)
 
|[[#Ben Fehrman (University of Chicago  | TBA ]]
 
| Lin
 
|-
 
|March 30
 
| Spring recess Mar 28-Apr 5 (S-N)
 
|[[#  |  ]]
 
|
 
|-
 
|April 6
 
|
 
|[[#  |  ]]
 
|
 
|-
 
|April 13
 
|
 
|[[#  |  ]]
 
|
 
|-
 
|April 20
 
|Yuan Lou (Ohio State)
 
|[[#Yuan Lou (Ohio State) | TBA]]
 
|Zlatos
 
|-
 
|April 27
 
|
 
|[[#  |  ]]
 
|
 
|-
 
|May 4
 
|
 
|[[#  |  ]]
 
|
 
|-
 
|}
 
  
  
== Abstracts ==
+
== 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. 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
 +
 
 +
2.
 +
 
 +
'''Week 10 (11/1/2020-11/7/2020)'''
  
===Jun Kitagawa (Toronto)===
+
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be
  
Regularity theory for generated Jacobian equations: from optimal transport to geometric optics
+
2.
  
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.
 
  
===Jessica Lin (Madison)===
+
{| cellpadding="8"
 +
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|- 
 +
|}
  
Algebraic Error Estimates for the Stochastic Homogenization of Uniformly Parabolic Equations
+
== Abstracts ==
  
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.
+
===  ===
  
===Haozhao Li (University of Science and Technology of China)===
+
Title: 
Regularity scales and convergence of the Calabi flow
 
  
We define regularity scales to study the behavior of the Calabi flow.
+
Abstract:
Based on estimates of the regularity scales, we obtain convergence theorems
 
of the Calabi flow on extremal K\"ahler surfaces, under the assumption of global existence
 
of the Calabi flow solutions. Our results partially confirm Donaldson’s conjectural picture for
 
the Calabi flow in complex dimension 2. Similar results hold in high dimension with an extra
 
assumption that the scalar curvature is uniformly bounded.
 

Latest revision as of 14:36, 21 October 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. 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

2.

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.


date speaker title host(s)

Abstracts

Title:

Abstract: