Higher index theory and quantitative operator $K$-theory

Dapeng Zhou

16:20 pm to 17:10 pm, June 1st, 2015   Science Building A1414

Abstract:

Higher index theory are closely related to a range of mathematical issues including topology of manifold and metrics of positive scalar curvature. The Baum-Connes conjecture and the coarse Baum-Connes conjecture are algorithms to compute the higher indices of elliptic differential operators. The quantitative operator $K$-theory, a refined version of classical operator $K$-theory, is a powerful tool to study these conjectures.

In this talk, I will start with the basic de nitions and facts from higher index theory, and I will give a survey on recent development of Baum-Connes conjecture and quantitative $K$-theory method.