Event Type:

Department Colloquium

Date/Time:

Monday, November 10, 2014 - 16:00 to 17:00

Location:

Kidder 350

Local Speaker:

Abstract:

Smooth manifolds admitting metrics of positive and non-negative sectional curvature have played an important role in the history of Riemannian geometry. The interplay between geometric restrictions on a manifold such as admitting positive sectional curvature or an Einstein metric and topological properties of the manifold remains mysterious. Topological classifications of existing examples are the first steps in understanding this interplay.

After an overview of the history starting with Gauss and Riemann, I will discuss my work determining the topological classificationÂ of various families of smooth manifolds that are of interest to both differential geometers and theoretical physicists; most of these manifolds admit either Einstein metrics or metrics of positive or non-negative sectional curvature.