Algebraic Geometry Seminar

Yukinobu TodaKavli Institute for the Physics and Mathematics of the Universe
On d-critical birational geometry and categorical DT theories

Friday, October 23, 2020 - 9:00am
Zoom (email for link)

In this talk, I will explain an idea of d-critical birational geometry, which deals with certain `virtual' birational maps among schemes with d-critical structures. One of the motivations of this new framework is to categorify wall-crossing formulas of Donaldson-Thomas invariants. I will propose an analogue of D/K equivalence conjecture in d-critical birational geometry, which should lead to a categorification of wall-crossing formulas of DT invariants. The main result in this talk is to realize the above story for local surfaces. I will show the window theorem for categorical DT theories on local surfaces, which is used to categorify wall-crossing invariance of genus zero GV invariants, MNOP/PT correspondence, etc.