Geometric Analysis and Topology Seminar

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Universal Behaviors in Geometric Heat Flows

Speaker: Dan Knopf, UT Austin

Location: Warren Weaver Hall 517

Date: Friday, May 8, 2015, 11 a.m.

Synopsis:

Geometric heat flows like Ricci flow and mean curvature flow have proven to be remarkably successful tools to investigate the geometry and topology of manifolds. As is well known, these nonlinear PDE have a diffusion-reaction structure that makes them prone to finite-time singularities. But these singularities are aids, not obstacles, to these flows' applications, because regions of high curvature tend to be very special. In this talk, we will survey these phenomena and present evidence in favor of the conjectures that (1) solutions asymptotically acquire extra symmetries as they become singular, and (2) generic solutions may be constrained to a small catalog of universal asymptotic profiles.