R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
On d-critical Birational Geometry and Categorical DT Theories
Yukinobu Toda (IPMU)
Abstract:
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.
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