MS Seminar (Mathematics - String Theory)

Speaker: Hyeonjun Park (KIAS)
Title: Donaldson-Thomas theory of Calabi-Yau 4-folds via derived algebraic geometry
Date (JST): Tue, Mar 07, 2023, 13:30 - 15:00
Place: Hybrid
Abstract: In this talk, we revisit DT4 theory via the perspective of derived algebraic geometry. Conceptually, the Borisov-Joyce/Oh-Thomas virtual cycles for (-2)-shifted symplectic derived schemes are the fundamental cycles of quasi-smooth Lagrangians. I will first introduce a virtual pullback formula between these virtual cycles for Lagrangian correspondences. I will then explain deformation invariance in terms of the exactness of the symplectic forms. I will also explain Kiem-Li's cosection localization via (-1)-shifted closed 1-forms and their connection to DT4 theory through the twisted (-2)-shifted cotangent bundles. Finally, I will explain how to construct (-1)-shifted closed 1-forms by generalizing Pantev-Toen-Vaquie-Vezzosi's integration map, which provides the reduced virtual cycles for counting surfaces.
Remarks: Seminar room A & Zoom