Paul Hacking, University of Massachusetts, Amherst

Smoothing surface singularities via mirror symmetry

We use the Strominger-Yau-Zaslow interpretation of mirror symmetry to describe deformations of surface singularities in terms of counts of holomorphic curves and discs on a mirror surface, which are computed tropically. In particular we prove Looijenga's conjecture on smoothability of cusp singularities. This is joint work with Mark Gross and Sean Keel, and builds on work of Gross-Siebert and Gross-Pandharipande-Siebert

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