2022 UMN Summer Workshop on Analysis of PDEs

Advisory: 
Note that the workshop is intended for graduate students and advanced undergraduates.

Organizers: 

  • Hao Jia, University of Minnesota, Twin Cities

In this five-day workshop for both graduate students and advanced undergraduate students, there will be a number of lectures given by active and leading experts in several important areas of analysis of partial differential equations, especially those arising from mathematical analysis of fluid dynamics and nonlinear waves. Participants will learn about the physical background, rigorous mathematical formulation, analytic tools, and latest developments in important PDE phenomena including singularity formation, uniqueness and non-uniqueness of weak solutions, stability mechanisms, and soliton resolution. Participants will also have many opportunities to interact with the lecturers in informal settings.

We will provide financial support to facilitate students' participation. To apply, please submit the following documents through the Workshop Application link at the top of the page:

  1. A brief CV or resume.  (A list of publications is not necessary.);
  2. A reference letter from your advisor or professor.

Supported by NSF CAREER 1945179

Schedule

Subscribe to this event's calendar

Monday, July 25, 2022

9:00 am - 9:30 am Registration and Coffee Vincent 502
9:30 am - 10:30 am Instability and non-uniqueness in the Navier-Stokes equations

Dallas Albritton (Princeton University)

Vincent 570
10:30 am - 11:00 am Break and Discussion Vincent 502
11:00 am - 12:00 pm Singularity formation in incompressible fluids and related models

Jiajie Chen (California Institute of Technology)

Vincent 570
12:00 pm - 1:30 pm Lunch  
1:30 pm - 2:30 pm 1d scattering theory and its application to nonlinear dispersive equations

Gong Chen (Georgia Institute of Technology)

Vincent 570
2:30 pm - 3:00 pm Break Vincent 502
3:00 pm - 4:00 pm Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations

Hao Jia (University of Minnesota, Twin Cities)

Vincent 570
4:00 pm - 4:30 pm Break and Discussion Vincent 502

Tuesday, July 26, 2022

9:00 am - 9:30 pm Coffee Vincent 502
9:30 am - 10:30 am Instability and non-uniqueness in the Navier-Stokes equations

Dallas Albritton (Princeton University)

Vincent 570
10:30 am - 11:00 am Break and Discussion Vincent 502
11:00 am - 12:00 pm Singularity formation in incompressible fluids and related models

Jiajie Chen (California Institute of Technology)

Vincent 570
12:00 pm - 1:30 pm Lunch  
1:30 pm - 2:30 pm 1d scattering theory and its application to nonlinear dispersive equations

Gong Chen (Georgia Institute of Technology)

Vincent 570
2:30 pm - 3:00 pm Break and Discussion Vincent 502
3:00 pm - 4:00 pm Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations

Hao Jia (University of Minnesota, Twin Cities)

Vincent 570
4:00 pm - 5:00 pm Outdoor Group Activity

Wednesday, July 27, 2022

9:00 am - 9:30 am Coffee Vincent 502
9:30 am - 10:30 am Instability and non-uniqueness in the Navier-Stokes equations

Dallas Albritton (Princeton University)

Vincent 570
10:30 am - 11:00 am Break and Discussion Vincent 502
11:00 am - 12:00 pm Singularity formation in incompressible fluids and related models

Jiajie Chen (California Institute of Technology)

Vincent 570
12:00 pm - 1:30 pm Lunch  
1:30 pm - 2:30 pm 1d scattering theory and its application to nonlinear dispersive equations

Gong Chen (Georgia Institute of Technology)

Vincent 570
2:30 pm - 3:00 pm Break and Discussion Vincent 502
3:00 pm - 4:00 pm Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations

Hao Jia (University of Minnesota, Twin Cities)

Vincent 570
4:00 pm - 4:30 pm Break and Discussion Vincent 502

Thursday, July 28, 2022

9:00 am - 9:30 am Coffee Vincent 502
9:30 am - 10:30 am Instability and non-uniqueness in the Navier-Stokes equations

Dallas Albritton (Princeton University)

Vincent 570
10:30 am - 10:45 am Group Photo  
10:45 am - 11:00 am Break and Discussion Vincent 502
11:00 am - 12:00 pm On the long-term regularity of water waves

Alexandru Ionescu (Princeton University)

Vincent 570
12:00 pm - 1:30 pm Lunch  
1:30 pm - 2:30 pm On the long-term regularity of water waves

Alexandru Ionescu (Princeton University)

Vincent 570
2:30 pm - 3:00 pm Break and Discussion Vincent 502
3:00 pm - 4:00 pm Singularity formation in incompressible fluids and related models

Jiajie Chen (California Institute of Technology)

Vincent 570
4:00 pm - 4:30 pm Break and Discussion Vincent 502
4:30 pm - 5:00 pm Panel Discussion Vincent 570

 

Friday, July 29, 2022

8:30 am - 9:00 am Coffee Vincent 502
9:00 am - 10:00 am Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations

Hao Jia (University of Minnesota, Twin Cities)

Vincent 570
10:00 am - 10:30 am Break and Discussion Vincent 502
10:30 am - 11:30 am On the long-term regularity of water waves

Alexandru Ionescu (Princeton University)

Vincent 570

Participants

Name Department Affiliation
Dallas Albritton Institute for Advanced Studies Princeton University
Adam Black Department of Mathematics Yale University
Gong Chen Department of Mathematics Georgia Institute of Technology
Jiajie Chen Department of Applied and Computational Mathematics California Institute of Technology
Adriaan de Clercq School of Mathematics University of Minnesota, Twin Cities
Kevin Dembski Department of Mathematics Duke University
Samir Donmazov Department of Mathematics University of Kentucky
Ziyang Gao Mathematics University of Minnesota, Twin Cities
Jialun He Department of Mathematics State University of New York - Stonybrook
Yupei Huang Department of Mathematics Duke University
Alexandru Ionescu Department of Mathematics Princeton University
Hao Jia School of Mathematics University of Minnesota, Twin Cities
Aldis Kurmis Department of Mathematics University of Minnesota, Twin Cities
Noah Lee Department of Applied and Computational Mathematics Princeton University
Kexin Li Department of Mathematics University of Michigan
Zhengjun Liang Department of Mathematics University of Michigan
Jiaqi Liu Department of mathematics University of Southern California
Tal Malinovitch Department of Mathematics Yale University
Frederick Rajasekaran Department of Mathematics University of California, San Diego
Xuanlin Shu Department of Mathematics Rutgers, State University of New Jersey
Yixuan Wang Department of Applied and Computational Mathematics California Institute of Technology
Kin Yau James Wong Department of Mathematics University of California, San Diego
Yantao Wu Department of Mathematics Johns Hopkins University

 

Start date
Monday, July 25, 2022, 9 a.m.
End date
Friday, July 29, 2022, 11:30 a.m.
Location

University of Minnesota

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