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Special Colloquium - Eric Chen University of California, Berkeley

Event Type
Rui Antonio Loja Fernandes
Altgeld 245
Feb 29, 2024   4:00 - 4:50 pm  
Eric Chen
Rui Fernandes
Originating Calendar
Mathematics Colloquium & Named Lectures

Title: Features of Ricci flow smoothing and singularities in four dimensions

Abstract: The Ricci flow, introduced by Hamilton in the 1980s, is a geometric-analytic tool that has since found many applications including Perelman's resolution of the Poincaré and Thurston's Geometrization conjectures, which classify three-dimensional compact manifolds and generalize the classical uniformization theorem for two-dimensional surfaces. The flow is a parabolic evolution equation which tends to smooth out a Riemannian metric on a manifold, but it may also encounter singularities; both are important features which can help us understand the topology of the manifold.  When moving to four dimensions, conical singularities are an important new class of singularities that arise.  I will discuss work on the existence of asymptotically conical expanding Ricci solitons in dimension four, joint with Richard Bamler, which may play a role in resolving these singularities and help in the ongoing construction of a theory of four-dimensional Ricci flow with surgery for the purpose of new applications.

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