报告人：邓金涛(美国纽约州立大学布法罗分校)

时间：第一次    2024年06月18日 14:30   

          第二次    2024年06月21日 14:30    

          第三次    2024年06月25日 14:30    

          第四次    2024年06月27日 14:30 

地点：理科楼LA103  

摘要：The geometry and topology of a smooth closed manifold is governed by certain elliptic differential operators. These operators are Fredholm operators, and their Fredholm indices can be calculated by the famous Atiyah-Singer index formula. A central question in mathematics is to extend the Atiyah-Singer index theory to non-compact manifolds. In the non-compact case,the solution spaces of elliptic operators can be infinite-dimensional. Thus, the classic Fredholm index is not well defined. A generalization of the Fredholm index, called the higher index, can be defined in the framework of noncommutative geometry. The higher index can be used to study the geometry and topology of a manifold, for instance, the problem of existence of Rimeannian metric with positive scalar curvature. However, the higher indices are hard to compute. The Baum-Connes conjecture provides an algorithm to compute the higher index for an elliptic operator on a non-compact manifold.

I am planning to give 4 lectures, and I will talk about the following:

简介：邓金涛，美国纽约州立大学布法罗分校博士后。

邀请人：数学研究中心

欢迎广大师生积极参与！