The coarse Baum-Connes conjecture and controlled operator $K$-theory

Dapeng Zhou  (Vanderbilt University)

10:00 am to 11:00 am, Dec 25th, 2013   Science Building A1510

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 controlled 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 definitions and facts from higher index theory, and I will give a survey on recent development of coarse Baum-Connes conjecture and controlled $K$-theory method.