GT seminar: "Quantum Decorated Character Varieties"

Abstract: Character varieties parametrize G-local systems on manifolds, for G a reductive group. It's sometimes natural to consider manifolds equipped with a patchwork of local systems for different groups, leading to a need for defects in character varieties. When the patchwork consists of G and its maximal torus T, the resulting moduli space is called a decorated character variety. These appear in the definition of cluster coordinates, in the study of irregular connections, and in the construction of a knot invariant known as the A-polynomial. In all of these cases there is physical motivation to understand the quantized version. We will introduce character varieties and explain a skein theoretic approach to quantizing them with or without defects. The quantization of the A-polynomial will serve as our main motivation and a running example. This is based on joint work in progress with David Jordan.

This is a talk in the geometry and topology seminar series.