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Width, scalar curvature and macroscopic scalar curvature

By Yevgeny Liokumovich

Gromov observed a surprising interplay between positive scalar curvature and a simple condition on the volumes of balls of fixed radius known as positive macroscopic scalar curvature. I will talk about some results about Urysohn width and lengths of closed geodesics in PSC and PMSC spaces, and how ideas travel back and forth between these two worlds.

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