Speaker: Michael Hartglass (UC Berkeley)

Title: Rigid C* tensor categories of bimodules over interpolated free group factors

Date/Time: January 16 (Wed.), 2013, 3:55-4:55

Room: 118 Math. Sci. Building

Abstract: The notion of a fantastic planar algebra will be presented and some examples will be given. I will then show how such an object can be used to diagrammatically describe a rigid, countably generated C^* tensor category C. Following in the steps of Guionnet, Jones, and Shlyakhtenko, I will present a diagrammatic construction of a II₁ factor M and a category of bimodules over M which is equivalent to C. Finally, I will show that the factor M is an interpolated free group factor and can always be made to be isomorphic to L(F_∞). Therefore we will deduce that every rigid, countably generated C^* tensor category is equivalent to a category of bimodules over L(F_∞). This is joint work with Arnaud Brothier and David Penneys.