Structure & Description

This mini course is combined with 2023 HDAG workshop. We will have 4 invited lecturers to give mini-courses of 3 lectures each. The topics of the mini-courses focus on derived geometry and birational geometry.

Talk Time (Agenda)

3/13 13:30-14:30

3/15 09:00-10:00

3/16 15:00-16:00

Lecture I: Donaldson-Thomas theory and wall-crossing (video)

Abstract: I will give an overview of Donaldson-Thomas invariants counting points or curves on Calabi-Yau 3-folds and their wall-crossing formula. I will focus on the MacMahon formula for counting points and DT/PT correspondence for counting curves. I will also give motivations toward categorifications of DT invariants and wall-crossing formula.

Lecture II: Categorical Donaldson-Thomas theory for quivers with super-potentials (video)

Abstract: I will introduce categorical DT theory for quivers with super-potentials, and explain basic tools of its study, e.g. window theorem, categorical Hall products. I will then focus on specific quivers called DT/PT quivers, which appear as Ext-quivers for DT/PT wall-crossing on Calabi-Yau 3-folds, and give a categorical analogue of DT/PT correspondence via semiorthogonal decomposition. This is a joint work with Tudor Padurariu.

Lecture III: Categorical Donaldson-Thomas theory for local surfaces (video)

Abstract: I will give a definition of categorical DT theory for local surfaces, i.e. the total spaces of canonical line bundles on surfaces, based on Koszul duality and singular support theory. I will then give semiorthogonal decompositions of DT categories into PT categories and quasi-BPS categories, using the result for the DT/PT quiver. This is a joint work with Tudor Padurariu.