C*-superrigidity

Abstract: A discrete group is called C*-superrigid, if it can be recovered from its reduced group C*-algebra. This notation parallels W*-superrigidty for von Neumann algebras. Motivated by Higman's unit conjecture for complex group rings, one can ask whether every torsion-free group is C*-superrigid. Surprisingly until 2017 the only known examples of torsion-free C*-superrigid groups were abelian. In this talk, I will introduce you to the concept and motivation of C*-superrigidity. Subsequently, I will describe developments around this topic since 2017, and exemplify relevant ideas through my joint work with Caleb Eckhardt, which shows that all finitely generated, torsion-free, 2-step nilpotent groups are C*-superrigid. I will end the talk by sharing my perspective on the future of the topic.

operator algebras

Audience: researchers in the topic

Comments: Assumed Knowledge: Basics of operator algebras.

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UK Virtual operator algebras seminar

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