PDE Geometric Analysis seminar

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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

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.