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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2006-2007 MATHEMATICS COLLOQUIUM SERIES 01/22/07 Colloquium Dr. Corey Hoelscher University of Pennsylvania Cohomogeneityone manifolds and non-negative sectional curvature Abstract:  A cohomogeneityone manifold can be thought of as a manifold which is slightly less homogeneous than a homogeneous space. More precisely, they are manifolds with an action of a compact lie group such that the orbit space is one dimensional. Recently, Grove-Zillerconstructed metrics of non-negative sectional curvature on a large class of cohomogeneityone manifolds. I will start by giving an overview of the study of non-negative curvature followed by an introduction to cohomogeneityone manifolds. I will conclude by presenting a classification of compact simply connected cohomogeneityone manifolds in dimensions 5, 6 and 7 and discussing its application to non-negative curvature.