The geometry and topology of manifolds with positive spectrum

In this talk, I will discuss my recent joint work with Jiaping Wang. The class of manifolds being considered are complete manifolds whose Ricci curvature is bounded from below and the bottom of the spectrum of the Laplacian is positive. An important quantity is the ratio between the lower bound of the Ricci curvature and the bottom of the spectrum. There are two critical values for this ratio, each one gives a metric rigidity theorem and also some topological restriction on this class of manifolds. In particular, one can derive a generalization of a theorem of Witten and Yau.

Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).