Jakub Curda

C*-superrigidity of a certain class of torsion free groups

Given a countable discrete group G, one can construct a group C*-algebra from its left regular representation. Whenever G is amenable, this object captures the representation theory of G. It is natural to ask how much information is remembered by this construction. In some cases, everything about the group is remembered and such groups are called C*-superrigid.
It is an open question whether all torsion free groups are C*-superrigid. In this talk I will focus on the class of finitely generated, torsion free, virtually abelian groups, which are the fundamental groups of certain flat Riemannian manifolds. Whenever the group has a specific form or the dimension of the manifold is small, the group is C*-superrigid. This talk is based on joint work with S. Knudby, S. Raum, H. Thiel, and S. White.