Yang Zhou:Quasimap wall-crossing and applications

Abstract: The theory of Gromov-Witten invariants is a curve counting theory defined by integration on the moduli of stable maps. Varying the stability condition gives alternative compactifications of the moduli space and defines similar invariants. One example is epsilon-stable quasimaps, defined for a large class of GIT quotients. When epsilon tends to infinity, one recovers Gromov-Witten invariants. When epsilon tends to zero, the invariants are closely related to the B-model in physics. The space of epsilons has a wall-and-chamber structure, and a wall-crossing formula was conjectured by Ciocan-Fontanine and Kim. In this talk, I will explain the wall-crossing phenomenon, sketch a proof of the wall-crossing formula and discuss its variants and applications.