The K-theory of Roe algebras and the coarse Baum-Connes conjecture

Speaker:Jintao Deng (University of Waterloo, Canada)

Date:November 1 Mon. 9:00am -- 11:00am

Venue: ZOOM ID: 978479233

Abstract:The coarse Baum-Connes conjecture claims that a certain assembly is an isomorphism. It has important applications in the study of the existence of a metric with positive scalar curvature and the Novikov conjecture on the homotopy invariance of the higher signature on a manifold. In this talk, I will talk about the Roe algebras which encode the large-scale geometry of a metric space. The higher index of an elliptic operator is an element of the K-theory of this algebra. The coarse Baum-Connes conjecture provides an algorithm to compute its $K$-theory. I will talk about our recent result that the coarse Baum-Connes conjecture holds for the relative expanders constructed by Arzhantseva and Tessera which is not coarsely embeddable into Hilbert space. I will also talk about a recent result on the equivariant coarse Baum-Connes conjecture.