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Thursday, November 30, 2023 - 4:30pm

Yi Lai

Stanford University

Location

University of Pennsylvania

4C8 DRL

Ricci flow is an important tool in geometric analysis. There have been remarkable topology applications of Ricci flow on closed manifolds, such as the Poincaré Conjecture resolved by Perelman, and the recent Generalized Smale Conjecture resolved by Bamler-Kleiner. In contrast, much less is known about the Ricci flow on open manifolds. Solitons produce self-similar Ricci flows, and they often arise as singularity models. Collapsed singularities and solitons create additional difficulties for open manifolds. In this talk, I will survey some recent developments in Ricci flow on open manifolds. In particular, I will talk about the resolution of Hamilton's Flying Wing Conjecture, and the resulting collapsed steady solitons.