Operator Theory Seminar
A group $G$ is $W^*$-superrrigid if it can be completely reconstructed from its von Neumann algebra $L(G)$. Producing such examples is a very important problem in von Neumann algebras as it distills the very classification of these objects. While this problem can be traced all the way to the pioneers of the field, currently less than three classes of $W^*$-superrigid groups are known in the literature.
In my talk I will highlight several constructions in group theory (direct products, iterations of amalgams and HNN-extensions, semidirect products with non-amenable core) that lead to new examples $W^*$-superrigid groups.
Along the way I will point out several applications of these results to the classification of non-amenable $C^*$-algebras as well.
This is based on a joint a recent work with Alec Diaz-Arias and Daniel Drimbe.