ALEXANDER BORIS Goncharov: Quantum symmetry via Quantum Geometry of moduli spaces #ICBS2024

I will discuss moduli spaces P(G,S), which parametrise flat G-bundles on topological surfaces S with boundary, equipped with some boundary data. The boundary data allows to promote the operation of surface gluing to the gluing maps of related moduli spaces. The moduli spaces P(G,S) carry canonical cluster Poisson structure, functorial in S, and compatible with the gluing maps. I will explain how quantum symmetry, including quantum groups and their representations, emerge naturally from the geometry and cluster quantization of these moduli spaces. This talk is based on the joint work with Linhui Shen.