Cluster quantization from factorization homology

Abstract: The character variety of a manifold is its moduli space of flat G-bundles. These moduli spaces and their quantizations appear in a number of places in mathematics, representation theory, and quantum field theory. Famously, Fock and Goncharov showed that a certain "decorated" variant of character varieties carries the structure of a cluster variety -- that is, the moduli space contains a distinguished set of toric charts, with combinatorially defined transitions functions (called mutations). This led them to a now-famous quantization of their decorated character varieties.

In this talk I'll explain that the by-hands construction of these charts by Fock and Goncharov can in fact be extracted from a more general framework called stratified factorization homology, and I'll outline how this allows us to extend the Fock-Goncharov story from surfaces to 3-manifolds.

category theoryquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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