Background: Dr James Thompson is postdoctoral researcher at the Mathematics Research Unit at the University of Luxembourg, working in the research group of Prof. Dr Anton Thalmaier. He completed his PhD in 2016 at the University of Warwick, under the supervision of Prof. Xue-Mei Li. His research interests include the study of diffusion processes on manifolds, particularly heat kernels, Brownian bridges and derivative formulae.

 

 Title: Brownian motion on a Riemannian manifold

 

 Abstract: In this talk, our discussion will center on a stochastic process, called Brownian motion, in the geometric setting of a Riemannian manifold. We will explain why the study of this object is useful and interesting, summarizing some recent results.  These include a heat kernel formula, a differentiation formula for the associated semigroup and some gradient estimates. This talk is intended as an introduction to the topic, so some proofs will be omitted, the focus being on providing an accessible account of the key ideas.