中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 李超 博士 （NYU Courant）

题  目：The geometry and topology of scalar curvature

时  间：2022.09.23（星期五），09:00-10:00

地  点：腾讯会议：867-143-901        

摘  要：Scalar curvature is a weak curvature invariant of Riemannian metrics, making its effects on the geometry and topology of a manifold rather delicate. In this talk, I will survey some classical and recent results towards understanding such effects. In particular, I will discuss the macroscopic geometry of manifolds with positive scalar curvature, and its two applications: the solution to the K(pi, 1) conjecture in dimensions 4 and 5, as well as the stable Bernstein theorem for minimal hypersurfaces in R^4. Part of this talk is based on joint work with Otis Chodosh.