Speaker: Sébastien Falguières

Title: The representation Category of any compact group is the Bimodule Category of a type II1 factor.

Abstract: The C*-tensor Category Bimod(M) consisting of all finite index M-M-bimodules over a type II1 factor M is a very rich invariant of the factor. Indeed, it encodes, for example, the outer automorphism group Out(M) and the fundamental group F(M). In general, Bimod(M) is very hard to compute. The aim of this talk is to present examples of type II1 factors with prescribed bimodule Category: we prove that given any compact group G, there exists a minimal action of G on a II1 factor M such that the bimodule Category of the fixed-point II1 factor MG is naturally equivalent with the representation category of G.