Groups and Operator Algebras Seminar

Speaker: Jamie Gabe (University of Southern Denmark, Odense)

Title: Simple AF embeddability for unimodular group C*-algebras

Abstract: For any locally compact group G, the left regular (unitary) representation generates a C*-algebra of bounded operators on the Hilbert space L^2(G). J. Rosenberg proved in the 80's that a discrete group G is amenable provided its induced C*-algebra forms a quasidiagonal set of operators on L^2(G), and he conjectured that the converse also holds. The conjecture was confirmed in 2015 by Tikuisis, White, and Winter, and using methods of Ozawa, Rørdam, and Sato for elementary amenable groups, they showed the stronger result that such group C*-algebras embed into a simple approximately finite-dimensional (AF) C*-algebra. I will report on some developments on how to extend this result to locally compact unimodular groups.

GOA website: https://sites.google.com/view/copenhagen-goa-seminar