Event Type:

Analysis Seminar

Date/Time:

Tuesday, June 5, 2012 - 08:00

Location:

Kidder 356

Abstract:

We will discuss the Laplacian $\Delta$ as an introduction to analysis on Riemannian manifolds. In particular, we will see how the spectral properties of this operator depend upon the geometry of the underlying manifold, introduce the corresponding Riesz and Bessel potential (Sobolev) spaces, and study some properties of the heat kernel, that is, the integral kernel of the heat semigroup formed by $\exp(-t\Delta)$. This last object plays a basic role in areas ranging from number theory to topology to PDEs. This talk will be accessible and of interest to anyone interested in geometry or analysis.