EVENT DETAILS AND ABSTRACT

Title: Modular functors and higher Teichmuller theory
Speaker: Gus Schrader
Speaker Info: Columbia University
Brief Description: Virtual (Zoom) Talk (email for passcode)
Special Note:
Abstract:

In the approach to the construction of invariants of links in 3-manifolds pioneered by Witten, a crucial role is played by the notion of a modular functor. Such a functor assigns to a surface a finite dimensional representation of its mapping class group in a way that is compatible with gluing surfaces together along a boundary circle. I'll report on joint work with A. Shapiro in which we prove the conjecture of Fock and Goncharov that the quantization of moduli spaces of local systems on hyperbolic surfaces, a.k.a. higher Teichmuller theory, delivers an infinite dimensional analog of such a modular functor. I'll conclude by describing some applications of our construction to the representation theory of non-compact quantum groups.