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Postdoctoral Seminar December 11, 2009
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Location: MSRI: Simons Auditorium
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Maksim Maydanskiy
Title: Building Landau-Ginsburg superpotentials
Abstract: Landau-Ginsburg models appear as mirrors to Fano manifolds. I will give some examples of how such models are constructed, following the work of Auroux and Fukaya-Oh-Ohta-Ono.

Benjamin Thorsten Nill
Title: A simple condition for a projective toric manifold to have dual defect
Abstract: In 2006 Sandra Di Rocco classified all n-dimensional smooth lattice polytopes whose associated projective toric manifolds have dual defect (i.e., the dual variety is not a hypersurface). These lattice polytopes can be characterized by the vanishing of a certain combinatorial invariant, namely, the degree of the A- discriminant. In joint work with Alicia Dickenstein we show that there is another equivalent combinatorial condition: the given n-dimensional smooth polytope multiplied by a factor of {(n+2)/2} has no lattice points in its interior. This was recently proved under a strong additional hypothesis by Dickenstein, Di Rocco and Piene. Our result confirms a general conjecture of Beltrametti and Sommese on polarized complex varieties in the toric case.

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