Geometric Analysis and Topology Seminar

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Rigidity Results in Scalar Curvature

Speaker: Yipeng Wang, Columbia University

Location: Warren Weaver Hall 512

Date: Friday, November 1, 2024, 11 a.m.

Synopsis:

A central theme in Gromov's program is the exploration of the implications of metric geometry for spaces with scalar curvature bounded from below. Inspired by Toponogov's triangle comparison theorem on manifolds with nonnegative sectional curvature, Gromov postulated a conjecture regarding the scalar curvature extremality property of convex polytopes. In his 'Four Lectures', he also outlined a proof based on a smoothing procedure. In this talk, I will discuss some recent progress on this problem, as well as several aspects of its generalizations.