EVENT DETAILS AND ABSTRACT

Title: Laplace Operator and the Topology of Complete Manifolds
Speaker: Professor Peter Li
Speaker Info: University of Califronia, Irvine
Brief Description:
Special Note:
Abstract:

In this talk, we will discuss how the Laplace operator is used to determine certain topological information of a complete non-compact manifold. Hodge theory asserts that when a manifold is compact, then its homology group can be computed using harmonic forms. Unfortunately, a similar theory does not exist for non-compact manifolds. However, for certain situations, one can still control some topological aspect using the analytic property of the Laplace operator. An example of this is a generalization of a theorem of Witten-Yau.