Eric Zaslow : Ribbon Graphs and Mirror Symmetry

Posted by , part of the Algebraic Geometry Seminar.

At

Aug. 26, 2010, 4 p.m.

In

SEO 636

Abstract

The moment map of the complex projective plane is a triangle. Generalizing this familiar observation somewhat, I will describe a correspondence between equivariant coherent sheaves on toric varieties and polyhedrally constant sheaves on vector spaces. Specializing to one dimension, I will then describe how to assign a category to a ribbon graph by appropriately gluing sheaves on the real line. The ribbon graph category is conjecturally equivalent to the Fukaya category of the Riemann surface described by the graph. A glued version of the correspondence above allows us to prove that the ribbon graph category is equivalent to the category of coherent sheaves on a "mirror" algebraic curve. I will develop the necessary mathematics from a *very* simple example. This talk is based on joint work with Bohan Fang, Chiu-Chu Melissa Liu, Nicolo' Sibilla and David Treumann.