What is … a Wasserstein distance?

This page hosts information on Matthias Liero's talk "What is … a Wasserstein distance?" at the "What is …?" seminar. The talk will take place on Friday, November 29, 1:00pm at TU MA544. This talk will help you better understand the talk by Martin Burger, which will start at 2pm at TU MA005.

Abstract

Gradient flows are an important subclass of evolution equations. A gradient-flow structure can be exploited to obtain additional information about the evolution, such as existence and the stability of solutions. Moreover, gradient flows can provide additional physical and analytical insight, such as the maximum dissipation of entropy and energy, or the geometric structure induced by the dissipation distance.

A special subclass is formed by gradient flows with respect to the Wasserstein distance. This class was first identified in the seminal work by Jordan, Kinderlehrer, and Otto in the late nineties. In my talk I will introduce the Wasserstein distance and discuss its relation to diffusion equations.

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