Speaker: Eric Chen (University of California, Berkeley)
Time: 09:00-10:20, Dec 21, 2023
Room: zoom meeting ID: 896 5812 5945, password: 290152
Tencent meeting ID: 942 663 0176, no password (if zoom cannot work)
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 Geometrization conjectures in dimension three. The flow evolves a Riemannian metric on a smooth manifold according to a parabolic evolution equation, and both its smoothing and singularity behaviors are important features which can help classify the topology of the manifold. I will discuss how smoothing properties of the flow lead to integral curvature pinching results near space forms in dimensions three and higher, in part joint with Guofang Wei and Rugang Ye. I will also 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 conical singularities of the flow, and help in the ongoing construction of a theory of Ricci flow with surgery in dimension four for potentially new topological applications.
