Algebraic Geometry Seminar
Eric Zaslow
Northwestern
Ribbon Graphs and Mirror Symmetry
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.
Thursday August 26, 2010 at 4:00 PM in SEO 636