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"Soap bubbles and topological obstructions to positive scalar curvature"

Geometry-Topology Seminar

Thursday, November 19, 2020 - 4:30pm

Otis Chodosh

Stanford University

Location

University of Pennsylvania

via Zoom

The Zoom link is: https://upenn.zoom.us/j/91890239234 This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (mmerling@math.upenn.edu), Davi Maximo (dmaxim@math.upenn.edu) or Herman Gluck (gluck@math.upenn.edu).

Title: Soap bubbles and topological obstructions to positive scalar curvature 

 

Abstract: The Geroch conjecture (proven by Schoen—Yau and Gromov—Lawson) says that there does not exist a metric of positive scalar curvature (PSC) on the 3-torus. I will explain how to generalize this in certain directions using soap bubbles (minimizers of a prescribed mean curvature functional). In particular I will explain why a closed 5-dimensional aspherical manifold does not admit a PSC metric. This is joint work with Chao Li.