Skein algebras and quantized Coulomb branches
数学专题报告
报告题目(Title)：Skein algebras and quantized Coulomb branches
报告人(Speaker)：Dylan Allegretti（清华大学）
地点(Place)：后主楼1223
时间(Time)：12月11日下午15:00-16:00
邀请人(Inviter)：肖杰、覃帆、周宇、方杰鹏、兰亦心
报告摘要
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.
