The University of Arizona
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Modular functor from higher Teichmüller theory

Algebraic Geometry Seminar

Modular functor from higher Teichmüller theory
Series: Algebraic Geometry Seminar
Location: ENR2 S395
Presenter: Alexander Shapiro, UC Berkeley

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 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 based on joint works with Gus Schrader.