Noncommutative Geometry Seminar

In joint work with A. Guionnet (and further joint work in progress with A. Guionnet and Y. Dabrowski) we construct an analog of Brenier's monotone transport in the non-commutative case. This is done by analyzing a non-commutative Monge-Ampere PDE. Among applications of our work are isomorphisms between C* and W*-algebras associated to certain classes of free Gibbs states. In particular, so-called q-deformed free group factors of Bozejko and Speicher are isomorphic to free groups factors if |q| is sufficiently small.