Smoothing surface singularities via mirror symmetry

Smoothing surface singularities via mirror symmetry

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Paul Hacking, University of Massachusetts, Amherst
Fine Hall 322

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. 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.