Abstract: Given an n-dimensional manifold (with n at least 4), it is generally impossible to control the topology of a homologically minimizing hypersurface M. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a 4-manifold X with natural curvature conditions (e.g. positive scalar curvature), provided that X admits certain embeddings into a homeomorphic S^4. As an application, we obtain black hole topology theorems in such 4-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.

Brief biography: Chao Li is an assistant professor at Courant Institute of Mathematical Sciences, New York University. Previously, he was an instructor at Princeton University. He got his Ph.D. at Stanford University. His dissertation advisors are Rick Schoen and Brian White. Before that he was an undergraduate student at Peking University, where he got his Bachelor's degree in Mathematics, mentored by Huijun Fan. His research is supported in part by the National Science Foundation and a Sloan research fellowship.

His research interests include differential geometry, partial differential equations, and geometric measure theory. Specifically, his recent work concerns minimal surfaces, scalar curvature and mathematical general relativity.

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