Harvard-MIT Algebraic Geometry Seminar

Tuesday, December 06, 2022 at 4:30pm to 5:30pm

Building 2, MIT Room 2-132
182 MEMORIAL DR, Cambridge, MA 02139

Featured Speaker: Tasuki Kinjo (University of Tokyo)

Title: Cohomological Donaldson-Thomas theory for 2-Calabi--Yau categories.

Abstract:  Cohomological Donaldson-Thomas (CoDT) invariants were introduced by Kontsevich-Soibelman and Brav-Bussi-Dupont-Joyce-Szendroi as categorifications of the Donaldson-Thomas invariants counting objects in 3-Calabi-Yau categories. In this talk, I will explain applications of the CoDT theory to the cohomological study of the moduli of objects in 2-Calabi-Yau categories. Among other things, I will construct a coproduct on the Borel-Moore homology of the moduli stack of objects in these categories and establish a PBW-type statement for the Kapranov-Vasserot cohomological Hall algebras. This talk is based on a joint work in progress with Ben Davison.

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