Working Seminar: Groups and Operator Algebras

Speaker: Henning Milhøj

Title: Traces, quasitraces, and Kaplansky's conjecture

Abstract: This talk will revolve around Kaplansky's conjecture stating that all quasitraces are traces. We will look at the current best known answers to this conjecture, as well as to the related question of when C*-algebras admit (quasi)traces and introduce numerical quantities measuring this property. Lastly, we will construct a C*-algebra, which arises as an ultraproduct of non-quasitracial C*-algebras, yet admits a quasitrace, and discuss its possible use in resolving Kaplansky's conjecture.

The talk will be elementary and does not require any prior knowledge on the subject.