Alexander Shapiro, Univ. of California, Berkeley, Modular functor from higher Teichmüller theory
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…