12-21【Eric Chen】Aspects of Ricci flow smoothing and singularities in higher dimensions


报告人:Eric Chen(加利福尼亚大学伯克利分校


地点:zoom会议号:896 5812 5945,密码:290152

           腾讯会议号:942 663 0176,无需密码(备用)

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.