Manifolds with positive sectional curvature

W. Ziller, University of Pennsylvania

Although manifolds with positive curvature have been a frequent subject in global Riemannian geometry, not much is known about obstructions and there are also very few known examples. I will discuss some candidates for new examples in dimension 7, which are, surprisingly, connected to other geometries such as self dual Einstein orbifolds, fatness of bundles, and 3-Sasakian geometry.