Melanie Pivarski

Melanie Pivarski
Ph.D. (2006) Cornell University

First Position

Visiting assistant professor at Texas A&M University


Heat Kernels on Euclidean Complexes


Research Area:
Probability and Analysis

Abstract: In this thesis we describe a type of metric space called an Euclidean polyhedral complex. We define a Dirichlet form on it; this is used to give a corresponding heat kernel. We provide a uniform small time Poincaré inequality for complexes with bounded geometry and use this to determine uniform small time heat kernel bounds via a theorem of Sturm. We then consider such complexes with an underlying finitely generated group structure. We use techniques of Saloff-Coste and Pittet to show a large time asymptotic equivalence for the heat kernel on the complex and the heat kernel on the group.