Operator Theory Semimar
A few years ago in a landmark paper, Guionnet and Shlyakhtenko proved the existence of free monotone transport from the joint law of a free semicircular family. In particular, these results imply that the von Neumann algebra (resp. $C^*$-algebra) generated by a free semicircular family is isomorphic to the von Neumann algebra (resp. $C^*$-algebra) generated by self-adjoint operators with a joint law "close" to the semicircle law in a certain sense. Notably, the von Neumann algebra generated by a free semicircular family is a free group factor. In this talk, I will discuss how to obtain corresponding results for the interpolated free group factors using an operator-valued framework. This is joint work with Michael Hartglass.