Recruitment Talk -- Macroscopic scalar curvature and the minimizing hypersurface trick

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December 5, 2022
4:15PM - 5:15PM
Location
CH240

Date Range
Add to Calendar 2022-12-05 16:15:00 2022-12-05 17:15:00 Recruitment Talk -- Macroscopic scalar curvature and the minimizing hypersurface trick Speaker:  Hannah Alpert Title: Macroscopic scalar curvature and the minimizing hypersurface trick Abstract: If the curvature of a closed manifold has a positive lower bound, how does that constrain the topology?  If it has a negative lower bound and complicated topology, how does that constrain the volume?  We consider the macroscopic cousins of these questions, meaning that instead of a lower bound on curvature, we require an upper bound on volumes of balls of a given radius in the universal cover of the manifold.  In many cases the macroscopic questions are better resolved than the original questions, and surprisingly, many of the proofs rely on One Weird Trick of locally comparing an area-minimizing hypersurface to a sphere. CH240 Department of Mathematics math@osu.edu America/New_York public
Description

Speaker:  Hannah Alpert

Title: Macroscopic scalar curvature and the minimizing hypersurface trick

Abstract: If the curvature of a closed manifold has a positive lower bound, how does that constrain the topology?  If it has a negative lower bound and complicated topology, how does that constrain the volume?  We consider the macroscopic cousins of these questions, meaning that instead of a lower bound on curvature, we require an upper bound on volumes of balls of a given radius in the universal cover of the manifold.  In many cases the macroscopic questions are better resolved than the original questions, and surprisingly, many of the proofs rely on One Weird Trick of locally comparing an area-minimizing hypersurface to a sphere.

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