Speaker: Mark Shoemaker (Colorado State University)
Title: Integral transforms and quantum correspondences
Abstract: I will re-frame a collection of well-known comparison results in genus zero Gromov-Witten theory in order to relate these to integral transforms between derived categories. The most well known of these comparisons is the crepant transformation conjecture, which describes a correspondence between the Gromov-Witten theory of K-equivalent spaces related by variation of GIT. It has been shown in many cases that this correspondence is compatible, in a precise way, with a Fourier-Mukai functor between the derived categories of the two spaces. In this talk I will discuss 3 other comparison results in Gromov-Witten theory, and in each case describe the corresponding functor between derived categories. This leads to a proof that a refined version of the crepant transformation conjecture implies the Landau-Ginzburg/Calabi-Yau correspondence.