Quantum Symmetry via Quantum Geometry of Moduli Spaces

Explore the intricate world of moduli spaces P(G,S) in this 1-hour 6-minute conference talk by ALEXANDER BORIS Goncharov at BIMSA. Delve into the parametrization of flat G-bundles on topological surfaces with boundary, and discover how boundary data enables the promotion of surface gluing to gluing maps of related moduli spaces. Examine the canonical cluster Poisson structure carried by P(G,S) moduli spaces, its functoriality in S, and compatibility with gluing maps. Uncover the natural emergence of quantum symmetry, including quantum groups and their representations, from the geometry and cluster quantization of these moduli spaces. Learn about the collaborative research with Linhui Shen that forms the foundation of this insightful presentation.