Degenerations, transitions and quantum cohomology

Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations helps with computing Gromov–Witten invariants, and the role of this story in Fanosearch programme. The challenge is to formulate enumerative symplectic geometry of complex $3$-folds in a way suitable for extracting invariants under blowups, contractions, and transitions.