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Regular version of the site

Working paper

Degenerations, transitions and quantum cohomology

arxiv.org. math. Cornell University, 2018. No. 1809.02737.
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.