Séminaires : Séminaire d'Algèbre

Character varieties of surfaces are fundamental objects in modern mathematics, appearing in low-dimensional topology, representation theory, and mathematical physics, among other areas. Given a reductive algebraic group G, the G-character variety of a surface is a moduli space parametrizing G-local systems on the surface.
Character varieties of surfaces are expected to arise in physics as Coulomb branches of certain quantum field theories. A Coulomb branch is a kind of moduli space that was recently given a precise mathematical definition in the work of Braverman, Finkelberg, and Nakajima.
In this talk, I will focus on the SL(2,C)-character variety of a surface. It has a quantization given by a noncommutative algebra called the Kauffman bracket skein algebra. I will describe a precise relationship between skein algebras and quantized Coulomb branches, confirming the physics prediction in some cases. This is joint work with Peng Shan.

This talk will take place on Zoom only.