Abstract: 
In this talk I will begin with Talagrand's $T_2$ inequality for the Gaussian measure and recall its relationship with Poincar'e and log-Sobolev inequalities, a family of dimension-free inequalities which play an essential role in infinite dimensional analysis and in high dimension (as in machine learning).    The main purpose is to establish process-level Talagrand's $T_2$ or the weaker $W_1H$ with sharp constants for  McKean-Vlasov diffusion for large time, even in phase transition  regime; and to prove such inequalities for mean-field paricles systems in no phase transition regime, uniform in large time and in the number of particles. Our main tools are refined coupling techniques and path-level Dobrushin's interdependence coefficients.
This talk is based on my past and recent joint works with Patrick Cattiaux, Hacene Djellout, Arnaud Guillin, Christian Leonard, Wei Liu, Boris Nectoux, Yutao Ma, Nian Yao, Chaoen Zhang.    


Bio-Sketch: 

Professor Liming Wu is a Professor of Mathematics at Université Clermont Auvergne in France and a Chair Professor at the Institute for Advanced Study in Mathematics, Harbin Institute of Technology. He has held a professorship in Clermont-Ferrand since 1993 and has been affiliated with HIT since 2021. He was a Changjiang Scholar at Wuhan University from 2000 to 2010 and a QianRen / Thousand Talents Scholar at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, from 2010 to 2015. Professor Wu is a probabilist whose research centers on large deviations, stochastic analysis, Markov processes and semigroups, spectral theory, logarithmic Sobolev and concentration inequalities, Malliavin calculus on Poisson spaces, and stochastic algorithms, with applications to statistical mechanics, sampling, and related problems in high-dimensional probability.