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Tuesday, March 08, 2016
4:00 PM - 5:00 PM
East Bridge 201 (Richard P. Feynman Lecture Hall)

Mathematics Colloquium

Towards homological mirror symmetry for hypersurfaces in toric varieties
Denis Auroux, Professor, Mathematics, UC Berkeley,

We will discuss some recent (and not-so-recent) progress on a program to establish Kontsevich's homological mirror symmetry conjectures for hypersurfaces in (C*)^N and, by extension, in toric varieties. We will first review a geometric construction of mirrors of these hypersurfaces, which turn out to be toric Landau-Ginzburg models.

In this limited setting, we define a fiberwise wrapped Fukaya category of the Landau-Ginzburg model and show (by constructing a mirror to the structure sheaf, or of other line bundles) that the derived category of the hypersurface embeds into it. This is joint work in progress with Mohammed Abouzaid.

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