Alexandre Minets (IST Austria), Cohomological Hall algebras and sheaves on surfaces

Abstract:

I will start with a quick survey of classical and cohomological Hall algebras. For that, I will recall how combinatorics of the Hilbert scheme of points on a plane are governed by the action of elliptic Hall algebra. In the second part of the talk, I will explain how certain aspects of this story can be generalized to the moduli spaces of sheaves on other surfaces, such as cotangent bundle to a curve.