3d cohomological Hall algebras for local surfaces
Organizers
Speaker
Adeel Khan
Time
Thursday, March 28, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
For a smooth surface $S$, Kapranov and Vasserot constructed a Hall algebra structure on the Borel-Moore homology of the moduli stack of (compactly supported) coherent sheaves on $S$. We construct a 3-dimensional refinement of this algebra associated with the canonical bundle $K_S$. This is achieved via a microlocal interpretation of cohomological Donaldson-Thomas invariants of local surfaces, to which end we develop a new theory of microlocalization in the context of derived stacks. Based on forthcoming joint work with Tasuki Kinjo.