Speaker：Hang Wang（East China Normal University）

Time：2022-06-06, 10:00

Location：Tencent Meeting ID：325906799（Pwd:202206）

Abstract:

Topological K-theory of a discrete group appears to be the left-hand side of the Baum-Connes conjecture and is claimed to give an algorithm for computing the K-theory of reduced group C^*-algebras via the higher index maps. The formulation of the topological K-theory for discrete groups naturally includes analytic indices for elliptic operators. From studying its Chern character and pairing with cyclic cocycle of the group algebra, we obtain index formulas that capture the information of the left-hand side of the Baum-Connes conjecture. On the way we obtain an equivariant Grothendieck-Riemann-Roch theorem. This is joint work with Paulo Carrillo-Rouse and Bai-Ling Wang.