COLLOQUIUM DI MATEMATICA ROMA TRE Prof. Arnaud Guillin Universite' Blaise Pascal Titolo: When Lyapunov meets Poincare' and (log-) Sobolev Mercoledi' 25 Maggio 2016 ORE 16:00 Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Aula F, primo piano, edificio Aule - Largo San Leonardo Murialdo,1 Abstract: Functional inequalities such as Poincare' or log-Sobolev inequalities have proved to be crucial in various fields, enabling to prove concentration of measure, speed of convergence to equilibrium, contractivity properties... and so much more, for example linked to curvature dimension condition. In probability, completely different techniques based on return time to nice set established via Lyapunov conditions and coupling enable to establish convergence to equilibrium. We will present here both approach, and their fundamental properties, and will finally link them in a (nice ? and) novel way.