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Explore the intriguing relationship between positive scalar curvature and positive macroscopic scalar curvature in this 39-minute lecture by Yevgeny Liokumovich from the University of Toronto. Delve into Gromov's observations on the connection between positive scalar curvature and the volumes of fixed-radius balls. Examine results concerning Urysohn width and closed geodesic lengths in PSC and PMSC spaces, and discover how concepts transfer between these two domains. Gain insights into cutting-edge research in differential geometry and its applications to understanding the structure of space.
