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Graduate Seminar

Lijiang Wu
Carnegie Mellon University
Title: Introduction to optimal transport

Abstract: In this talk, we introduce the so called Wasserstein metric on the space of probability measures on Polish spaces by optimal transport. We start from Monge's problem, which is to minimize the cost of transporting a given amount of homogeneous material mass from the given set of origins to the given set of destinations. By briefly discussing the issues with Monge's problem, we then move to its relaxation, Kantorovitch's problem, and show the well-posedness of the relaxed variational problem. The Monge-Kantorovitch problem induces the Wasserstein metric on the space of probability measures. We close the presentation with some properties of the metric and its applications in PDEs.

Date: Thursday, November 7, 2013
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell