May 29, 2023 to June 2, 2023
Paul Sabatier University, Toulouse
Europe/Paris timezone

Nathael Gozlan: Transport-Entropy forms of direct and reverse Santalo type inequalities

Jun 1, 2023, 11:10 AM
Paul Sabatier University, Toulouse

Paul Sabatier University, Toulouse

Institut de Mathématiques de Toulouse 118, route de Narbonne - Bat. 1R3 F-31062 Toulouse Cedex 9


Nathael Gozlan


In this talk, we will present new equivalent formulations of direct and converse Santalo inequalities involving the relative entropy functional
and various optimal transport costs. We will explore this connection on various model probability spaces. We will see in particular that the Mahler conjecture for the volume product of convex bodies is equivalent to sharp bounds on the deficit in the logarithmic Sobolev inequality for the Gaussian measure or for the uniform probability measure on the unit Euclidean sphere. Based on joint works with Matthieu Fradelizi, Shay Sadowsky and Simon Zugmeyer.

Presentation materials