# Difference between revisions of "PDE Geometric Analysis seminar"

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+ | |February 17 (joint with Analysis Seminar, 4:00 p.m., B139) | ||

+ | |Chanwoo Kim (Madison) | ||

+ | |[[#|Chanwoo Kim (Madison) | Hydrodynamic limit from the Boltzmann to the Navier-Stokes-Fourier ]] | ||

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|February 23 | |February 23 | ||

|Jennifer Beichman (Madison) | |Jennifer Beichman (Madison) |

## Revision as of 11:26, 18 January 2015

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

## Contents

### Previous PDE/GA seminars

### Tentative schedule for Fall 2015

# Seminar Schedule Spring 2015

date | speaker | title | host(s) | ||||
---|---|---|---|---|---|---|---|

January 21 (Departmental Colloquium: 4PM, B239) | Jun Kitagawa (Toronto) | Regularity theory for generated Jacobian equations: from optimal transport to geometric optics | Feldman | ||||

January 26 | |||||||

February 2 | Jessica Lin (Madison) | TBA | Kim | ||||

February 9 | |||||||

February 16 | |||||||

February 17 (joint with Analysis Seminar, 4:00 p.m., B139) | Chanwoo Kim (Madison) | Chanwoo Kim (Madison) | Hydrodynamic limit from the Boltzmann to the Navier-Stokes-Fourier | February 23 | Jennifer Beichman (Madison) | TBA | Kim | |

March 2 | Benoit Pausader (Princeton) | TBA | Kim | ||||

March 9 | |||||||

March 16 | |||||||

March 23 | |||||||

March 30 | Spring recess Mar 28-Apr 5 (S-N) | ||||||

April 6 | |||||||

April 13 | |||||||

April 20 | Yuan Lou (Ohio State) | TBA | Zlatos | ||||

April 27 | |||||||

May 4 |

## Abstracts

### Jun Kitagawa (Toronto)

Regularity theory for generated Jacobian equations: from optimal transport to geometric optics

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.