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Superrigidity for group operator algebras

Banff International Research Station for Mathematical Innovation and Discovery

It is a classical problem to recover a discrete group from various rings or algebras associated with it, such as the integral group ring. By analogy, in an operator algebraic framework we want to recover torsion-free groups from certain topological completions of the complex group ring, such as the reduced group $C^*$-algebra. Groups for which this is possible are called $C^*$-superrigid. My talk will discuss how a group can be recovered from its group rings, before I introduce the reduced group $C^*$-algebras and describe the state-of-the-art in $C^*$-superrigidity. I will end with a short account on other kinds of superrigidity for group operator algebras putting the subject into a bigger perspective.

Mathematics; Functional analysis; Dynamical systems and ergodic theory

video/mp4

Author affiliation: Stockholm University

2020-03-31

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73862

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/