Speaker: Sergey Galkin
Title: Minuscule varieties and mirror symmetry (joint work with Alexey Bondal)
Date: Nov 14, 2013, 14:00-16:00
Place: CINVESTAV
Abstract:
Minuscule varieties is a class of the simplest homogeneous manifolds,
it consists of Grassmannians, quadrics, maximal isotropic Grassmannians, two more exceptional examples, and their products. These varieties enjoy a minuscule descent: a variety of lines passing through a point on a minuscule variety is itself either a minuscule variety, or their product, or union. We use this construction to construct a mirror partner to each of these varieties, thus generalizing a construction of Eguchi-Hori-Xiong for Grassmannians. Then using methods of tropical geometry we prove the mirror symmetry, in what concerns count of rational curves and differential equations.