学术报告（李向东 2025.10.28）

摘要：In 1974, P. Malliavin introduced the Stochastic Calculus of Variations and gave a probabilsitic proof of the H\"ormander hypoellipticity theorem. Since then, the Malliavin calculus has been a central topic in stochastic analysis. The purpose of this talk is to use the Malliavin calculus to study thegeometric Langevin processesin connection with the kinetic Fokker-Planck equation on the cotangent bundle over compact Riemannian manifolds. We present an integration by parts formula and the gradient formula for the kinetic Fokker-Planck semigroup on the cotangent bundle of a compact Riemannian manifokd. Our results extend previous ones due to Bismut and P. L. Lions et al.