QM Research Seminar: Categorified quantum group representations from Fukaya-Seidel categories

Speaker: Elise Lepage (​Columbia University).

Abstract: 
Quantum groups and their representations admit categorifications, in which vector spaces and linear maps are replaced by categories and functors. I will describe a construction of these categorifications using Fukaya-Seidel categories of Coulomb branches. This construction realizes categorifications of irreducible representations, Verma modules, and arbitrary tensor products of these representations. A key feature of this construction is a differential relating categorified Verma modules to categorified irreducible representations. I will show how this differential arises geometrically.