Analysis of Fluids and Related Topics: Winding of Brownian trajectories and heat kernels on covering spaces, Speaker: Gautam Iyer

Analysis of Fluids and Related Topics
  • Gautam Iyer
  • Carnegie Mellon University
  • Winding of Brownian trajectories and heat kernels on covering spaces
Dec 7, 2017
4:30 pm
Fine Hall 322

Title:  Winding of Brownian trajectories and heat kernels on covering spaces

Abstract:

We study the long time behaviour of the heat kernel on Abelian covers of compact Riemannian manifolds. For manifolds without boundary work of Lott and Kotani-Sunada establishes precise long time asymptotics. Extending these results to manifolds with boundary reduces to a "cute" eigenvalue minimization problem, which we resolve for a Dirichlet and Neumann boundary conditions. We will show how these results can be applied to studying the "winding" of Brownian trajectories in Riemannian manifolds.