December 8, 2006

Mohammed Abouzaid (University of Chicago)

Title: Homological Mirror Symmetry for Toric Varieties

Abstract: I will begin by explaining the statement of the Homological Mirror Symmetry conjecture for Fano toric varieties and outline how Lefschetz fibrations have been used to prove the conjecture in some cases. I will then show how Mikhalkin's flavour of tropical geometry can be used to prove half of the homological mirror conjecture for all smooth projective toric varieties (dropping the Fano condition!). Time permitting, I will briefly describe how the tropical approach can also be used to address the case of Calabi-Yau hypersurfaces.