Mathematics

The classification of compact manifolds with non-negative sectional curvature is a long-standing and classic question in Riemannian geometry. For dimension greater or equal to 4, the question is widely open. In this talk we will introduce the audiences with some well-known obstruction theorems for a manifold to have (or to not have) non-negative curvature, then we will talk about the program of classifying non-negatively and positively curved manifolds with large isometric torus action. This has been a successful approach since the famous Hsiang-Kleiner's theorem in 1989.