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Cluster quantization is a procedure proposed by Fock and Goncharov for quantizing decorated character varieties -- these are moduli spaces of G-local systems on S equipped with B-reductions and T-framings in prescribed boundary regions. Their key observation is that compatible triangulations of S lead to simple toric charts on the classical moduli space, and these have obvious "log-canonical" quantizations, and can be glued combinatorially via cluster mutation.

Factorization homology is a powerful and rather general machine for producing invariants of manifolds. In this talk I'll explain a new construction of decorated character stacks and their quantizations ,using stratified factorization homology. This takes as basic input the categories Rep_q(G), Rep_q(B) and Rep_q(T), of representations of the quantum group, the quantum Borel, and the quantum Cartan, and "integrates" them over the stratified manifold. Our main result is to exhibit within our quantizations a full reflective subcategory, or "quantum open subset", which recovers the Fock-Goncharov quantization.

Zoom seminar info sent by email. Contact tudor@math.ucdavis.edu with any questions.