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This joint IAS/PU Groups and Dynamics Seminar features a talk by Alena Erchenko from Dartmouth College on the monotonicity of data along Ricci flow on surfaces. Explore the behavior of topological entropy, Liouville entropy, and mean root curvature for negatively curved metrics on closed surfaces of genus greater than or equal to 2. Learn about Manning's 2004 discovery that topological entropy strictly decreases along the normalized Ricci flow for variable negative curvature metrics, and discover Erchenko's answer to Manning's question about whether monotonicity holds for Liouville entropy. The presentation reveals that Liouville entropy strictly increases along the flow, based on joint work with Butt, Humbert, and Mitsutani. The seminar takes place at 4:30pm in Simonyi 101 on April 22, 2025.
