3d cohomological Hall algebras for local surfaces | BIMSA AG Seminar

Abstract

For a smooth surface S, Kapranov and Vasserot constructed a Hall algebra structure on theBorel-Moore homology of the moduli stack of (compactly supported) coherent sheaves on S. Weconstruct a 3-dimensional refinement of this algebra associated with the canonical bundle Ks. Thisis achieved via a microlocal interpretation of cohomological Donaldson-Thomas invariants of localsurfaces, to which end we develop a new theory of microlocalization in the context of derivedstacks. Based on forthcoming joint work with Tasuki Kinjo.