Speaker: Pavel Mnev
University of Notre Dame
Will give a Felix Klein Seminar entitled:
A gluing formula for heat kernels
Abstract: Let M be a Riemannian manifold split by a codimension 1 submanifold gamma into two manifolds with boundary M1 and M2. I will explain a formula allowing one to recover the heat kernel of the Laplacian on M in terms of heat kernels of Laplacians on M1 and M2 (with Dirichlet boundary condition on gamma) and the heat kernel on gamma itself. Time permitting, I will also explain a combinatorial counterpart (or "toy model") of this result, replacing manifolds with graphs; in this setup the gluing formula also admits a nice path-sum interpretation. The talk is based on a joint work with Konstantin Wernli https://arxiv.org/pdf/2404.
Date: 04-11-2024
Time: 2:00 pm
Location: 125 Hayes Healey Bldg