Time:
April 22nd, 10:30-11:30am
Location:
7A1
Speaker:
Alexander Grigor'yan (Universität Bielefeld)
Title:
HIMIS Colloquium - Analysis on Riemannian manifolds and volume growth
Abstract:
This is a survey of the results relating the volume growth of a Riemannian manifold $M$ to various properties of elliptic and parabolic PDEs on $M$ as well as to the behavior of Brownian motion on $M$. In particular, we discuss sufficient conditions for recurrence and stochastic completeness of Brownian motion, as well as the estimates for escape rate. We will also discuss heat kernel bounds, existence of global solutions of elliptic Schroedinger and semilinear PDEs, etc.
Bio:
Prof. Grigor'yan earned his Ph.D. from Moscow State University in 1982 under the supervision of Prof. Eugene Landis. Before joining the University of Bielefeld, he held positions at several prestigious institutions, including Imperial College London. His research interest lies in geometric analysis on Riemannian manifolds, graphs, and metric spaces.