Difference between revisions of "PDE Geometric Analysis seminar"

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(Charles Smart (MIT))
(PDE GA Seminar Schedule Fall 2020-Spring 2021)
 
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The seminar will be held  in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
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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]]===
 
===[[Previous PDE/GA seminars]]===
 +
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
== Seminar Schedule Spring 2012 ==
 
{| cellpadding="8"
 
!align="left" | date 
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | host(s)
 
|-
 
|Feb 6
 
|Yao Yao (UCLA)
 
|[[#Yao Yao (UCLA)|
 
Degenerate diffusion with nonlocal aggregation: behavior of solutions]]
 
|Kiselev
 
|-
 
|March 12
 
| Xuan Hien Nguyen (Iowa State)
 
|[[#Xuan Hien Nguyen (Iowa State)|
 
Gluing constructions for solitons and self-shrinkers under mean curvature flow]]
 
|Angenent
 
|-
 
|March 21(Wednesday!), Room 901 Van Vleck
 
|Nestor Guillen (UCLA)
 
|[[#Nestor Guillen (UCLA)|
 
The local geometry of maps with c-convex potentials]]
 
|Feldman
 
|-
 
|March 26
 
|Vlad Vicol (University of Chicago)
 
|[[#Vlad Vicol (U Chicago)|
 
Shape dependent maximum principles and applications]]
 
|Kiselev
 
|-
 
|April 9
 
|Charles Smart (MIT)
 
|[[#Charles Smart (MIT)|
 
TBA]]
 
|Seeger
 
|-
 
|April 16
 
|Jiahong Wu (Oklahoma)
 
|[[#Jiahong Wu (Oklahoma State)|
 
The 2D Boussinesq equations with partial dissipation]]
 
|Kiselev
 
|-
 
|May 14
 
|Jacob Glenn-Levin (UT Austin)
 
|[[#Jacob Glenn-Levin (UT Austin)|
 
TBA]]
 
|Kiselev
 
|}
 
  
==Abstracts==
 
  
===Yao Yao (UCLA)===
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== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==
''Degenerate diffusion with nonlocal aggregation: behavior of solutions''
+
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. 
  
The Patlak-Keller-Segel (PKS) equation models the collective motion of
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'''Week 1 (9/1/2020-9/5/2020)'''
cells which are attracted by a self-emitted chemical substance.  While the
 
global well-posedness and finite-time blow up criteria are well known, the
 
asymptotic behaviors of solutions are not completely clear.  In this talk I
 
will present some results on the asymptotic behavior of solutions when
 
there is global existence. The key tools used in the paper are
 
maximum-principle type arguments as well as estimates on mass concentration
 
of solutions. This is a joint work with Inwon Kim.
 
  
===Xuan Hien Nguyen (Iowa State)===
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1. Paul Rabinowitz - The calculus of variations and phase transition problems.
 +

https://www.youtube.com/watch?v=vs3rd8RPosA
  
''Gluing constructions for solitons and self-shrinkers under mean curvature flow''
+
2. Frank Merle - On the implosion of a three dimensional compressible fluid.
 +
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 
  
In the 1990s, Kapouleas and Traizet constructed new examples of minimal surfaces by desingularizing the intersection of existing ones with Scherk surfaces. Using this idea, one can find new examples of self-translating solutions for the mean curvature flow asymptotic at infinity to a finite family of grim reaper cylinders in general position. Recently, it has been shown that it is possible to desingularize the intersection of a sphere and a plane to obtain a family of self-shrinkers under mean curvature flow. I will discuss the main steps and difficulties for these gluing constructions, as well as open problems.
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'''Week 2 (9/6/2020-9/12/2020)'''
  
===Nestor Guillen (UCLA)===
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1. Yoshikazu Giga - On large time behavior of growth by birth and spread.
 +
https://www.youtube.com/watch?v=4ndtUh38AU0
  
We consider the Monge-Kantorovich problem, which consists in
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2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI
transporting a given measure into another "target" measure in a way
 
that minimizes the total cost of moving each unit of mass to its new
 
location. When the transport cost is given by the square of the
 
distance between two points, the optimal map is given by a convex
 
potential which solves the Monge-Ampère equation, in general, the
 
solution is given by what is called a c-convex potential. In recent
 
work with Jun Kitagawa, we prove local Holder estimates of optimal
 
transport maps for more general cost functions satisfying a
 
"synthetic" MTW condition, in particular, the proof does not really
 
use the C^4 assumption made in all previous works. A similar result
 
was recently obtained by Figalli, Kim and McCann using different
 
methods and assuming strict convexity of the target.
 
  
===Charles Smart (MIT)===
 
  
''PDE methods for the Abelian sandpile''
 
  
Abstract:  The Abelian sandpile growth model is a deterministic
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'''Week 3 (9/13/2020-9/19/2020)'''
diffusion process for chips placed on the $d$-dimensional integer
 
lattice.  One of the most striking features of the sandpile is that it
 
appears to produce terminal configurations converging to a peculiar
 
lattice.  One of the most striking features of the sandpile is that it
 
appears to produce terminal configurations converging to a peculiar
 
fractal limit when begun from increasingly large stacks of chips at
 
the origin.  This behavior defied explanation for many years until
 
viscosity solution theory offered a new perspective.  This is joint
 
work with Lionel Levine and Wesley Pegden.
 
  
===Vlad Vicol (University of Chicago)===
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1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
  
Title: Shape dependent maximum principles and applications
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2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
  
Abstract: We present a non-linear lower bound for the fractional Laplacian, when
 
evaluated at extrema of a function. Applications to the global well-posedness of active
 
scalar equations arising in fluid dynamics are discussed. This is joint work with P.
 
Constantin.
 
  
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{| cellpadding="8"
 +
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|- 
 +
|}
  
===Jiahong Wu (Oklahoma State)===
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== Abstracts ==
 
 
"The 2D Boussinesq equations with partial dissipation"
 
  
The Boussinesq equations concerned here model geophysical flows such
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=== ===
as atmospheric fronts and ocean circulations. Mathematically the 2D Boussinesq
 
equations serve as a lower-dimensional model of the 3D hydrodynamics
 
equations. In fact, the 2D Boussinesq equations retain some key features
 
of the 3D Euler and the Navier-Stokes equations such as the vortex stretching
 
mechanism. The global regularity problem on the 2D Boussinesq equations
 
with partial dissipation has attracted considerable attention in the last few years.
 
In this talk we will summarize recent results on various cases of partial dissipation,
 
present the work of Cao and Wu on the 2D Boussinesq equations with vertical
 
dissipation and vertical thermal diffusion,  and explain  the work of Chae and Wu on
 
the critical Boussinesq equations with a logarithmically singular velocity.
 
  
===Jacob Glenn-Levin (UT Austin)===
+
Title: 
  
TBA
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Abstract:

Latest revision as of 11:08, 13 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


date speaker title host(s)

Abstracts

Title:

Abstract: