This talk will be by videolink from Warsaw. The starting-time will be a little after 17:00 due to a TCC lecture and time needed to establish video connections.

Abstract: The Haagerup approximation property for finite von Neumann algebras (i.e.von Neumann algebras with a tracial faithful normal state) has been studied for more than 30 years. The original motivation to study this property came from the case of group von Neumann algebras of discrete groups, where it corresponds to the geometric Haagerup property of the underlying group. Last few years brought a lot of interest in the Haagerup property for discrete and general locally compact quantum groups. If the discrete quantum group in question is not unimodular, the associated (quantum) group von Neumann algebra cannot be finite, so we need a broader framework for the operator algebraic property. In this talk, I will present recent developments regarding the Haagerup approximation property for arbitrary von Neumann algebras and will also discuss some questions relating it to the issues related to the classical Schoenberg correspondence. (Mainly based on joint work with Martijn Caspers.)