题目：Geometric structures and new collapsing models of Einstein spaces 

报告人：Ruobing Zhang

(Stony Brook University)

Abstract : An Einstein manifold, by definition, has a Riemannian metric with constant Ricci curvature. Roughly, with some fixed gauge, the metric solves certain system of highly degenerate nonlinear elliptic PDEs. In both metric Riemannian geometry and geometric analysis, it is always a central topic to study the degeneration behaviors of a family of Einstein metrics and geometric evolutions of the underlying spaces. This talk centers on the geometric analysis of a family of collapsing Einstein manifolds with sufficiently wild analytic properties, for instance, the uniform Sobolev inequality never holds in any collapsing sequence. We will explain some entirely new tools from both metric-geometric and algebro-geometric sides in analyzing Einstein equations. Our specific concerns of the talk include the following:

(1) the sharp topological condition for the "existence" of the epsilon-regularity of collapsed Einstein metrics,

(2) geometric structures of collapsing Einstein limits,

(3) new constructions of collapsed Einstein spaces: in both low and high dimensional cases.

时间：4月19日（周五）下午16:00-17：00

地点：565net必赢客户端本部教二楼711教室

联系人：胥世成

欢迎全体师生积极参加！