Research talk · 1, 3 and 4 July 2025
Cohomological Hall algebras — exercise and research sessions
Summer School on Enumerative Geometry and Geometric Representation Theory, Università di Pisa
Abstract
Exercise session I: Examples of cohomological Hall algebras — 1 July 2025
After reviewing the six functors in the constructible derived category of an algebraic variety, I explain the construction of the cohomological Hall product at the sheaf-theoretic level and work through examples for quivers and preprojective algebras.
Exercise session II: Tools to study cohomological Hall algebras — 3 July 2025
I introduce dimensional reduction, BPS Lie algebras and the Poincaré–Birkhoff–Witt theorem as tools for investigating cohomological Hall algebras.
Research session: BPS Lie algebras and generalized Kac–Moody Lie algebras — 4 July 2025
I discuss the realization of the BPS Lie algebra of a preprojective algebra as a generalized Kac–Moody Lie algebra, based on joint work with Ben Davison and Sebastian Schlegel Mejia. I also describe the cohomological Hall algebra of the affine plane and possible structures for CoHAs in more general settings.