Colloquium Mathematics, Professor Mark A. Peletier (TUE)

Join us for coffee and tea at 15.30 p.m.

Date:                          Tuesday, May 14^th 2013

Speaker:                     Professor Mark A. Peletier (TUE)

Room:                         5161.0293 (Bernoulliborg)

Time:                           16.00

Title: Understanding the origins of the Wasserstein gradient flows

Abstract:

Many evolutionary systems described by parabolic partial differential equations can be written as a gradient flow of some energy with respect to some metric. When present, this gradient-flow structure provides both high-level insight into the behaviour of the system, and low-level, practical tools for the analysis of the system and its solutions.

Since the pioneering work of Jordan, Kinderlehrer, and Otto (1998) an impressive collection of evolutionary PDEs has been formulated as a gradient flow of some energy with respect to the Wasserstein metric.

In this talk I will briefly introduce the Wasserstein metric and the concept of a Wasserstein gradient flow, and then turn to the main topic of the talk. This is the question: how can we understand _why_ the Wasserstein metric appears in so many systems?

I will show how this gradient-flow structure is intimately connected to the large-deviation behaviour of systems of interacting particles. This connection gives us an explanation for the prevalence of Wasserstein gradient flows, and suggests directions for the derivation of a large number of related systems.

I will also describe more recent work, that illustrates how the same principles apply to non-particle stochastic systems, for instance systems in which energy is transported.

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and

Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl)

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/