Modular functor from higher Teichmüller theory

Alexander Shapiro (University of California, Berkeley)

Wednesday 11th December, 2019 16:00-17:00 Maths 311B


Quantized higher Teichmüller theory, as described by Fock and Goncharov, assigns an algebra and its representation to a surface and a Lie group. This assignment is equivariant with respect to the action of the mapping class group of the surface, and is conjectured to give an (infinite dimensional) analog of a modular functor, that is it should respect the operation of cutting and gluing of surfaces. In this talk I will outline a proof of the above conjecture, and explain how it is related to representation theory of quantum groups. This talk will be mostly based on joint works with Gus Schrader.

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