Please join us in welcoming Professor Pat McDonald from New College of Florida will visit our department on Tuesday, January 25.

Abstract: The heat content associated to a bounded domain in a Riemannian manifold is a function obtained by solving an initial value problem for the heat operator on the domain. Heat content gives rise to a collection of geometric invariants closely related to the Dirichlet spectrum. In this talk I will survey results that compare and contrast the role of heat content invariants to the role of spectral data in geometric analysis. In particular, I will discuss results involving planar polygons and provide explicit examples of where heat content invariants and Dirichlet spectrum behave similarly, and also where they behave differently.