June 22: Henry Liu

Title: Quasimaps and stable pairs

Abstract:

I will give a short introduction to the various flavors of moduli of 1-dimensional sheaves on threefolds (e.g. Donaldson-Thomas theory), all related by wall-crossing between certain stability chambers in the derived category. One such chamber, first studied by Bryan and Steinberg, yields the theory of pi-stable pairs. I will explain why pi-stable pairs and quasimaps are equivalent whenever they are comparable. Quasimaps have been used recently to study 3d mirror symmetry, which when pushed through this equivalence has implications for some aspects of sheaf-counting theories, including the (DT) crepant resolution conjecture. If time permits I'll discuss the proof of the equivalence, which explicitly matches vertices for the two theories using the derived McKay equivalence.