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Speculations about homological mirror symmetry for affine hypersurfaces

Presented by: 
Denis Auroux University of California, Berkeley
Tuesday 15th August 2017 - 10:00 to 11:00
INI Seminar Room 1
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.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons