The local categorical DT/PT correspondence


The DT/PT correspondence is a formula which relates Donaldson-Thomas invariants counting closed subschemes in Calabi-Yau 3-folds, and Pandharipnade-Thomas invariants counting stable pairs on them. It gives an economical way of formulating GW/DT correspondence by Maulik-Nekrasov-Okounkov-Pandharipande. The DT/PT correspondence was proved by wall-crossing in the derived category, where on the wall we have a special type of Ext-quivers called DT/PT quivers. In this talk, I will give a categorical wall-crossing formula for categories of matrix factorizations associated with DT/PT quivers. The resulting formula is a semiorthogonal decomposition which involves quasi-BPS categories, and is a categorical analogue of numerical DT/PT correspondence. This is a joint work with Tudor Padurariu.