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Speculations about homological mirror symmetry for affine hypersurfaces

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SYGW05 - Symplectic geometry - celebrating the work of Simon Donaldson

The wrapped Fukaya category of an algebraic hypersurface H in (C)n is conjecturally related via homological mirror symmetry to the derived category of singularities of a toric Calabi-Yau manifold whose moment polytope is determined by the tropicalization of H.  In this talk we will first explain the statement, and then discuss a conjectural enhancement to a “relative” version of homological mirror symmetry for the pair ((C)n, H). We will illustrate these ideas on simple examples such as pairs of pants.

This talk is part of the Isaac Newton Institute Seminar Series series.

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