Noncommutative Geometry Seminar

Date: May 1, 2023

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Jintao Deng, University of Waterloo

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

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.