For every discrete countable group acting properly on a metric space X by isometries, we associate the equivariant Roe algebra C*(X)^G: it is a Banach algebra that appears naturally in algebraic topology. Indeed, its K-theory groups contain the index of (abstract) elliptic pseudo-differential operators on X. The goal of this talk is to describe some cases when these K-theory groups can be computed, and describe some consequences for a variety of topological invariants. (Precisely, we will explain the case of SL(2,Z) acting on the Farey tree, which is a corollary of the Novikov conjecture for groups with Haagerup's property (see Higson-Kasparov and Tu) )

The talk will be given on Zoom. Please, contact the organizers for more information.