Hsian-Hua Tseng
The Ohio State University
Title
Fourier-Mukai equivalence and quantum differential equations
Abstract
Two smooth quasiprojective varieties X and X' are called K-equivalent if there is a birational map between them that preserves their canonical classes. The most famous example of this is the flop in dimension 3. When X and X' are K-equivalent, it is conjectured that their noncommutative geometries are the same, in the sense that their derived categories are equivalent, and such an equivalence is necessarily a Fourier-Mukai functor. It is also conjectured that their quantum geometries are the same, in the sense that their quantum cohomology rings are isomorphic. In this talk, we describe a conjecture, formulated by Iritani, that connects the two conjectures above. We also present some evidence.