PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephanie Zerby, Chun Liu.

Title:Optimal Transportation, Gradient Flows and Stochastic Evolutions
Seminar:Department of Mathematics Colloquium
Speaker:Karl-Theodor Sturm (Host: Yuxi Zheng), University of Bonn
Abstract:
We present a brief introduction to recent progress in optimal transportation and stochastic calculus on manifolds and metric spaces. We recall the characterization of diffusion equations on Riemannian manifolds M as gradient flows for generalized entropy functionals on the space of probability measures P(M), regarded as an infinite dimensional Riemannian manifold. Convexity properties of the relative entropy Ent(.|m) play an important role in a powerful concept of generalized Ricci curvature bounds for metric measure spaces (X, d, m). We illustrate new developments on super-Ricci flows for metric measure spaces and coupling properties of backward Brownian motions. Moreover, we present fundamental results for the Wasserstein diffusion, a canonical reversible process (µt)t≥0 on the space of probability measures P(R). This includes: particle approximation, logarithmic Sobolev inequaltiy, quasi-invariance of its invariant measure, the so-called entropic measure, P β. We also indicate how to construct the entropic measure on multi-dimensional spaces.

Room Reservation Information

Room Number:MB114
Date:02 / 26 / 2015
Time:03:30pm - 04:20pm