Sven Raum: C*-superrigidity of 2-step nilpotent groups

Abstract: A discrete group is called C*-superrigid, if it can be recovered from its reduced group C*-algebra.  Paralleling Higman's unit conjecture for complex group rings, one can ask whether every torsion-free group is C*-superrigid. This question appeared in print in an article of Ioana-Popa-Vaes in 2014. Surprisingly until 2017 the only know such examples of torsion-free C*-superrigid groups were abelian.
In this talk, I will describe the development around C*-superrigidity since 2017, and explain some aspects of my work with Caleb Eckhardt, showing that all finitely generated, torsion-free, 2-step nilpotent groups are C*-superrigid thereby exhibiting the first natural class of
non-abelian torsion-free C*-superrigd groups.