The talk is a report on joint work with Ben Davison and Lucien Hennecart.I will explain how to associate a generalised Kac—Moody algebra to any suffieciently geometric 2-Calabi—Yau category and relate it to the BPS algebra and thus Cohomological Hall algebra (CoHA) of the category. In particular, we get a structure theorem for the CoHA in terms of intersection cohomology of moduli spaces.
I will focus on the important special case of the category of representations of preprojective algebra of a quiver. Time permitting I will explain applications in non-abelian Hodge theory for stacks and enumerative geometry of sheaves on K3 surfaces.