Geometric and functional inequalities via OMT

Prof. Dr. Zoltán Balogh (Universität Bern)

Tuesday, 21 March, 13:15 - 15:00, HG G 43
Tuesday, 04 April, 13:15 - 15:00, HG G 43
Tuesday, 18 April, 13:15 - 15:00, HG G 43
Tuesday, 25 April, 13:15 - 15:00, HG G 43

The recordings can be found here on the ETH video portal.

Abstract

Optimal mass transport is a versatile tool that can also be used to prove sharp geometric and functional inequalities. The purpose of this minicourse is to present this technique in various settings. We start with Prekopa-Leindler and Borell-Brascamp-Lieb inequalites. Next, we derive hypercontractivity estimates for the solution of the Hamilton-Jacobi equations in connection with log-Sobolev inequalities. We continue with Talagrand transportation and concentration inequalities and finally we consider sharp Sobolev and Gagliardo-Nirenberg inequalities.