Algebra and Geometry Seminar

USC, Kaprelian Hall, Room 414

In this talk, I will present homological mirror symmetry with the complex side being a theta divisor in a principally polarized abelian variety and the symplectic side being a locally toric noncompact Calabi-Yau manifold, together with a complex valued function on it that is a symplectic fibration away from a singular fiber.  For example, a theta divisor in 1 complex dimension is a genus two curve.  We will also discuss the identifications between the complex and Kahler moduli spaces under mirror symmetry.  In addition, for genus two curves, we will talk about the Kahler cones in the mirror Kahler space and see that it in fact corresponds to the cones in the Voronoi decomposition for symmetric positive definite matrices.  This is a joint work in preparation with Haniya Azam, Catherine Cannizzo, and Chiu-Chu Melissa Liu.