Speaker: Ben Davison  (University of Edinburgh)

Title: Towards Hecke transformations for moduli of sheaves on surfaces

Abstract:

Certain enumerative invariants of moduli spaces of semistable coherent sheaves on surfaces, as well as moduli spaces of semistable Higgs bundles, exhibit a surprising independence from the Euler characteristic (chi-independence) of the coherent sheaves under consideration. The surprise is that for the right choice of invariants, this independence continues to hold even in the presence of strictly semistables, at which point the relevant moduli stacks may become very singular. In these talks I will report on joint work in progress with Tasuki Kinjo, aiming to explain this independence, at the cohomological level, with the aid of cohomological Hall algebras and (affinized) BPS Lie algebras. The goal of the project is to show that this chi-independence lifts to an isomorphism of cohomological BPS invariants, which in turn is realised via Hecke transformations on the BPS cohomology of coherent sheaves on 2-Calabi-Yau surfaces