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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===
+
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==
 
  
  
{| cellpadding="8"
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== 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.
 +

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.
|August 31 (FRIDAY),
+
https://www.youtube.com/watch?v=4ndtUh38AU0
| Julian Lopez-Gomez (Complutense University of Madrid)
 
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]
 
| Rabinowitz
 
  
|- 
+
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI
|September 10,
 
| Hiroyoshi Mitake (University of Tokyo)
 
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]
 
| Tran
 
|- 
 
|September 12 and September 14,
 
| Gunther Uhlmann (UWash)
 
|[[#Gunther Uhlmann | TBA ]]
 
| Li
 
|- 
 
|September 17,
 
| Changyou Wang (Purdue)
 
|[[#Changyou Wang |  Some recent results on mathematical analysis of Ericksen-Leslie System ]]
 
| Tran
 
|-
 
|Sep 28, Colloquium
 
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
 
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
 
| Thiffeault
 
|-
 
|October 1,
 
| Matthew Schrecker (UW)
 
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]
 
| Kim and Tran
 
|- 
 
|October 8,
 
| Anna Mazzucato (PSU)
 
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]
 
| Li and Kim
 
|- 
 
|October 15,
 
| Lei Wu (Lehigh)
 
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]
 
| Kim
 
|- 
 
|October 22,
 
| Annalaura Stingo (UCD)
 
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]
 
| Mihaela Ifrim
 
|- 
 
|October 29,
 
| Yeon-Eung Kim (UW)
 
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]
 
| Kim and Tran
 
|- 
 
|November 5,
 
| Albert Ai (UC Berkeley)
 
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]
 
| Mihaela Ifrim
 
|- 
 
|Nov 7 (Wednesday), Colloquium
 
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)
 
|[[#Nov 7: Luca Spolaor (MIT) |  (Log)-Epiperimetric Inequality and the Regularity of Variational Problems  ]]
 
| Feldman
 
|-
 
|December 3, ''' Time: 3:00, Room: B223 Van Vleck '''
 
| Trevor Leslie (UW)
 
|[[#Trevor Leslie | Flocking Models with Singular Interaction Kernels ]]
 
| Kim and Tran
 
|-
 
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''
 
|Serena Federico (MIT)
 
|[[#Serena Federico | Sufficient conditions for local solvability of some degenerate partial differential operators ]]
 
| Mihaela Ifrim
 
|-
 
|December 10, Colloquium, '''Time: 4:00'''
 
| [https://math.mit.edu/~maxe/ Max Engelstein] (MIT)
 
|[[# Max Engelstein| The role of Energy in Regularity ]]
 
| Feldman
 
|-
 
|January 28,
 
| Ru-Yu Lai (Minnesota)
 
|[[# Ru-Yu Lai | TBA ]]
 
| Li and Kim
 
|-
 
|January 29, '''4:00 p.m. in VV B139'''
 
| Trevor Leslie (UW-Madison)
 
|[[# Trevor Leslie| TBA ]]
 
| Analysis seminar
 
|-
 
| February 4,
 
|
 
|[[# | No seminar (several relevant colloquiums in Jan/30-Feb/8)]]
 
|
 
|-
 
| February 11,
 
| Seokbae Yun (SKKU, long term visitor of UW-Madison)
 
|[[# Seokbae Yun | TBA ]]
 
| Kim
 
|- 
 
| February 18,  '''Room: VV B239'''
 
| Daniel Tataru (Berkeley)
 
|[[# Daniel Tataru | TBA ]]
 
| Ifrim
 
|-                                                                                                                                                         
 
| February 19,
 
| Wenjia Jing (Tsinghua University)
 
|[[#Wenjia Jing | TBA ]]
 
| Tran
 
|-
 
|February 25,
 
| Xiaoqin Guo (UW)
 
|[[#Xiaoqin Guo | TBA ]]
 
| Kim and Tran
 
|-
 
|March 4
 
| Vladimir Sverak (Minnesota)
 
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]
 
| Kim
 
|-   
 
|March 11
 
| Jonathan Luk (Stanford)
 
|[[#Jonathan Luk | TBA  ]]
 
| Kim
 
|-
 
|March 18,
 
| Spring recess (Mar 16-24, 2019)
 
|[[#  |  ]]
 
 
|-   
 
|April 1
 
| Zaher Hani (Michigan)
 
|[[#Zaher Hani | TBA  ]]
 
| Ifrim
 
|-
 
|April 15,
 
| Yao Yao (Gatech)
 
|[[#Yao Yao | TBA ]]
 
| Tran
 
|-   
 
|April 22,
 
| Jessica Lin (McGill University)
 
|[[#Jessica Lin | TBA ]]
 
| Tran
 
|- 
 
|April 29,
 
| Beomjun Choi (Columbia)
 
|[[#Beomjun Choi  | Evolution of non-compact hypersurfaces by inverse mean curvature]]
 
|  Angenent
 
|}
 
  
== Abstracts ==
 
  
===Julian Lopez-Gomez===
 
  
Title: The theorem of characterization of the Strong Maximum Principle
+
'''Week 3 (9/13/2020-9/19/2020)'''
  
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes  a popular result of Berestycki, Nirenberg and Varadhan.
+
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
  
===Hiroyoshi Mitake===
+
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
Title: On approximation of time-fractional fully nonlinear equations
 
  
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.)
 
  
  
 +
'''Week 4 (9/20/2020-9/26/2020)'''
  
===Changyou Wang===
+
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
  
Title: Some recent results on mathematical analysis of Ericksen-Leslie System
+
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM
  
Abstract: The Ericksen-Leslie system is the governing equation  that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.
 
  
===Matthew Schrecker===
 
  
Title: Finite energy methods for the 1D isentropic Euler equations
+
'''Week 5 (9/27/2020-10/03/2020)'''
  
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.
+
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo
  
===Anna Mazzucato===
+
2.  Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c
  
Title: On the vanishing viscosity limit in incompressible flows
 
  
Abstract: I will discuss recent results on the  analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity  may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions.  I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.
+
'''Week 6 (10/04/2020-10/10/2020)'''
  
===Lei Wu===
+
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
  
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects
+
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
  
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.
 
  
 +
'''Week 7 (10/11/2020-10/17/2020)'''
  
===Annalaura Stingo===
+
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s
  
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D
+
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg
  
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms »  .
 
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.
 
  
===Yeon-Eung Kim===
+
'''Week 8 (10/18/2020-10/24/2020)'''
  
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties
+
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg
  
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.
+
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ
  
===Albert Ai===
+
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.
  
Title: Low Regularity Solutions for Gravity Water Waves
 
  
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.
+
'''Week 9 (10/25/2020-10/31/2020)'''
  
===Trevor Leslie===
+
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE
  
Title: Flocking Models with Singular Interaction Kernels
+
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
  
Abstract: Many biological systems exhibit the property of self-organization, the defining feature of which is coherent, large-scale motion arising from underlying short-range interactions between the agents that make up the system.  In this talk, we give an overview of some simple models that have been used to describe the so-called flocking phenomenon.  Within the family of models that we consider (of which the Cucker-Smale model is the canonical example), writing down the relevant set of equations amounts to choosing a kernel that governs the interaction between agents.  We focus on the recent line of research that treats the case where the interaction kernel is singular.  In particular, we discuss some new results on the wellposedness and long-time dynamics of the Euler Alignment model and the Shvydkoy-Tadmor model.
 
  
===Serena Federico===
 
  
Title: Sufficient conditions for local solvability of some degenerate partial differential operators
+
'''Week 10 (11/1/2020-11/7/2020)'''
  
Abstract: In  this  talk  we  will  give  sufficient  conditions  for  the  local  solvability  of  a  class  of degenerate second order linear partial differential operators with smooth coefficients. The class under consideration, inspired by some generalizations of the Kannai operator, is characterized by the presence of a complex subprincipal symbol. By giving suitable conditions on the subprincipal part and using the technique of a priori estimates,  we will show that the operators in the class are at least $L^2$ to $L^2$ locally solvable.
+
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be
  
===Max Engelstein===
+
2.
  
Title: The role of Energy in Regularity
 
  
Abstract: The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy.
+
{| cellpadding="8"
 +
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|-  
 +
|}
  
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field.
+
== Abstracts ==
  
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur.
+
===  ===
  
===Beomjun Choi===
+
Title:  
In this talk, we first introduce the inverse mean curvature flow and its well known application in the the proof of Riemannian Penrose inequality by Huisken and Ilmanen. Then our main result on the existence and behavior of convex non-compact solution will be discussed.  
 
  
The key ingredient is a priori interior in time estimate on the inverse mean curvature in terms of the aperture of supporting cone at infinity. This is a joint work with P. Daskalopoulos and I will also mention the recent work with P.-K. Hung concerning the evolution of singular hypersurfaces.
+
Abstract:

Latest revision as of 12:00, 25 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. 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.


date speaker title host(s)

Abstracts

Title:

Abstract: