Speaker: Song Yu (Columbia University)

Title: Open-closed duality via relative-local correspondence

Abstract: We discuss a mathematical approach to the open-closed duality proposed by Mayr, which is a correspondence in genus zero between open Gromov-Witten invariants of toric Calabi-Yau threefolds and closed Gromov-Witten invariants of toric Calabi-Yau fourfolds. We establish the correspondence in two steps: First, a correspondence between the open invariants and the relative Gromov-Witten invariants of relative Calabi-Yau threefolds, which follows from the topological vertex (Li-Liu-Liu-Zhou, Fang-Liu). Second, a correspondence between the relative invariants and the closed invariants, which gives an instantiation of the log-local principle of van Garrel-Graber-Ruddat in the non-compact setting. Our correspondences are base on localization. We also discuss generalizations and implications of our correspondences. Joint work with Melissa Liu.