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.