Algebraic Modular Functor in Higher Teichmuller Theory

Alexander Shapiro (Edinburgh, UK)

October 31, 2025 (in-person)

Abstract: Given a simple Lie group G and a surface S, one may consider the corresponding moduli space M_{G,S} of G-local systems on S. The latter carries a natural Poisson structure. Partial data of the higher Teichmuller theory is a construction of the quantum cluster algebra L_{G,S}, quantizing the Poisson algebra of functions O(M_{G,S}). In this talk I will outline a proof of the algebraic part of the modular functor conjecture, stating that the assignment of the algebra L_{G,S} to a surface S is functorial, i.e. it respects cutting and gluing. This is a joint work with Gus Schrader.