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]]===
===[[Spring 2015 | Tentative schedule for Spring 2015]]===
+
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
= Seminar Schedule Fall 2014 =
 
{| cellpadding="8"
 
!align="left" | date 
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | host(s)
 
|-
 
|September 15
 
|Greg Kuperberg (UC-Davis)
 
|[[#Greg Kuperberg (UC-Davis) |  ''Cartan-Hadamard and the Little Prince'' ]]
 
|Viaclovsky
 
|-
 
|-
 
|September 22 (joint with Analysis Seminar)
 
|Steve Hofmann (U. of Missouri)
 
|[[#Steven Hofmann (U. of Missouri) |    ''Quantitative Rectifiability and Elliptic Equations'']]
 
|Seeger
 
|-
 
|-
 
|Oct 6th,
 
|Xiangwen Zhang (Columbia University)
 
|[[#Xiangwen Zhang (Columbia University) | ''ALEXANDROV’S UNIQUENESS THEOREM FOR CONVEX SURFACES'']]
 
|B.Wang
 
|-
 
|-
 
|October 13
 
|Xuwen Chen (Brown University)[http://www.math.brown.edu/~chenxuwen/]
 
|[[#Xuwen Chen (Brown University) |
 
TBA]]
 
|C.Kim
 
|-
 
|-
 
|October 20
 
|Kyudong Choi (UW-Madison)
 
|[[#Kyudong Choi (UW-Madison) |
 
Finite time blow up for 1D models for the 3D Axisymmetric Euler Equations the 2D Boussinesq system]]
 
|C.Kim
 
|-
 
|-
 
|October 27
 
|Chanwoo Kim (UW-Madison)
 
|[[#Chanwoo Kim (UW-Madison) |
 
BV-Regularity of the Boltzmann Equation in Non-Convex Domains]]
 
|Local
 
|-
 
|-
 
|November 10
 
|Philip Isett (MIT)
 
|[[#Philip Isett (MIT) |  TBA ]]
 
|C.Kim
 
|-
 
|-
 
|November 17
 
|Lei Wu
 
|[[#Lei Wu | Geometric Correction for Diffusive Expansion in Neutron Transport Equation  ]]
 
|C.Kim
 
|-
 
|-
 
|November 24
 
|Hongnian Huang (Univeristy of New Mexico)
 
|[[#Hongnian Huang (UNM) |  TBA ]]
 
|B.Wang
 
|-
 
|}
 
  
== Fall Abstracts ==
 
  
===Greg Kuperberg===
+
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==
''Cartan-Hadamard and the Little Prince.''
+
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
 +
 
  
===Steve Hofmann===
+
'''Week 13 (11/22/2020-11/28/2020)'''
''Quantitative Rectifiability and Elliptic Equations''
 
  
A classical theorem of F. and M. Riesz states that for a simply connected domain in the complex plane with a rectifiable boundary, harmonic measure and arc length measure on the boundary are mutually absolutely continuous. On the other hand, an example of C. Bishop and P. Jones shows that the latter conclusion may fail, in the absence of some sort of connectivity hypothesis. In this talk, we discuss recent developments in an ongoing program to find scale-invariant, higher dimensional versions of the F. and M. Riesz Theorem, as well as converses. In particular, we discuss substitute results that continue to hold in the absence of any connectivity hypothesis.
+
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be
  
===Xiangwen Zhang===
+
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8
''ALEXANDROV’S UNIQUENESS THEOREM FOR CONVEX SURFACES''
 
  
A classical uniqueness theorem of Alexandrov says that: a closed strictly convex twice differentiable surface in R3 is uniquely determined to within a parallel translation when one gives a proper function of the principle curvatures. We will talk about a PDE proof for this thorem, by using the maximal principle and weak uniqueness continuation theorem of Bers-Nirenberg. Moreover, a stability result related to the uniqueness problem will be mentioned. This is a joint work with P. Guan and Z. Wang.
+
{| cellpadding="8"
If time permits, we will also briefly introduce the idea of our recent work on Alexandrov’s theorems for codimension two submanifolds in spacetimes.
+
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|-  
 +
|}
  
===Kyudong Choi===
+
== Abstracts ==
''Finite time blow up for 1D models for the 3D Axisymmetric Euler Equations the
 
2D Boussinesq system''
 
  
In connection with the recent proposal for possible singularity formation at the boundary for solutions of the 3d axi-symmetric incompressible Euler's equations / the 2D Boussinesq system (Luo and Hou, 2013), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data. This is joint work with T. Hou, A. Kiselev, G. Luo, V. Sverak, and Y. Yao.
+
===  ===
  
===Lei Wu===
+
Title: 
''Geometric Correction for Diffusive Expansion in Neutron Transport Equation''
 
  
We revisit the diffusive limit of a steady neutron transport equation in a 2-D unit disk with one-speed velocity. The traditional method is Hilbert expansions and boundary layer analysis. We will carefully study the classical theory of the construction of boundary layers, and discuss the necessity and specific method to add the geometric correction.
+
Abstract:

Latest revision as of 21:46, 22 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

date speaker title host(s)

Abstracts

Title:

Abstract: