On delocalised traces

15.04. bis 15.04.2026, 10:15  –  Campus Golm, Haus 9, Raum 1.22
Forschungsseminar: Gruppen und Operatoralgebren

Dr. Sanaz Pooya

Abstract:

Delocalised traces are tracial functionals on L¹(G) associated to conjugacy classes of a group G. When the conjugacy class is the identity, one recovers the von Neumann trace. For nontrivial conjugacy classes, however, these traces do not in general extend to the closure $C^*_r​(G)$.
In the case where G is hyperbolic, work of Puschnigg shows that one can nonetheless define pairings between such traces and $K_0​(C^*_r​(G))$. I will survey a few results on such trace pairings. In particular, I will discuss delocalised L²-Betti numbers and present some computations for virtually free groups.