“The coherent-constructible correspondence and homological mirror symmetry for toric varieties”
Melissa Liu, Columbia University

Abstract:
I will discuss (i) SYZ transformation relating equivariant coherent sheaves on a toric variety to Lagrangians in the cotangent of R^n, (ii) microlocalization functor relating the Fukaya category of the cotangent to constructible sheaves on the base (due to Nadler-Zaslow, Nadler), and (iii) a categorification of Morelli's theorem relating equivariant coherent sheaves on a toric variety to constructible sheaves on R^n. This talk is based on joint work with Bohan Fang, David Treumann and Eric Zaslow.