Smith Colloquium

November 30, 2017

Max Fathi, Institut de Mathematiques de Toulouse, France

Title: Optimal transport and evolution equations in spaces of probability measures

Abstract: In the past twenty years, it has been discovered that for many reversible Markov processes, the evolution of its law can be viewed as solving a gradient ODE with energy function V(x) for a well-chosen metric structure on the space of probability measures, defined via optimal mass transport.
In this talk, I will present this viewpoint, and how it can be used to study asymptotic behavior of sequences of Markov processes, with some applications to statistical physics. This will be based on works by Ambrosio, Gigli, Jordan, Kinderlehrer, Otto, Savare and Zambotti.

CAM Seminar Fall 2017 - Spring 2018