Functional inequalities for diffusion semi-groups

The aim of this reading seminar is to introduce the theory of logarithmic sobolev inequalities. This tool has a growing field of applications in Analysis, Probability and Geometry. The main subjects that we will focus on are: the introduction of these inequalities thanks to Bernoulli and Gaussian laws;  the notion of hypercontractivity; the curvature-dimension criteria. The lecture will mainly follow chapters 1 to 5 of the book by C. Ané, S. Blachère, D. Chafaï, P. Fougères, I. Gentil, F. Malrieu, C. Roberto, G. Scheffer (SUR LES INEGALITES DE SOBOLEV LOGARITHMIQUES).