Quasi-BPS categories

In this talk, I will explain the notion of "Quasi-BPS category". This is the (yet to be defined) category which categorifies BPS invariants on Calabi-Yau 3-folds, and plays an important role in categorical wall-crossing in Donaldson-Thomas theory. I will explain the motivation of quasi-BPS categories, give definition in the case of symmetric quivers with potential (a local model of CY 3-folds), and their properties. If time permits, I will explain quasi-BPS categories for local K3 surfaces and their relation to derived categories of hyperkahler manifolds. This is a joint work in progress with Tudor Padurariu.