COHA of zero dimensional sheaves on surfaces and the P=W conjecture

Abstract: Cohomological Hall algebras of 2CY categories feature in several recent geometric constructions of infinite dimensional quantum groups (such as affine Yangians) and their representations. The case of zero dimensional sheaves on smooth surfaces (such as projective surfaces, or line bundles over smooth projective curves) has attracted particular attention due to the analogy with usual Hecke operators (acting on moduli spaces of sheaves on curves as opposed to surfaces). We will describe the COHA in this case (a joint work with Mellit, Minets and Vasserot), and we will sketch its use in a recent proof of the P=W conjecture of de Catlado, Hausel and Migliorini relating the Hodge structure of character varieties and the perverse cohomology of the Hitchin fiibration (a joint work with Hausel, Mellit and Minets).

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar