Song Yu：Open/closed correspondence via relative/local correspondence
Abstract: We discuss a mathematical approach to the open/closed correspondence proposed by Mayr, which is a correspondence between the disk invariants of toric Calabi-Yau threefolds and genus-zero closed Gromov-Witten invariants of toric Calabi-Yau fourfolds. We establish the correspondence in two steps: First, a correspondence between the disk invariants and the genus-zero maximally-tangent 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 maximally-tangent relative invariants and the closed invariants, which can be viewed as an instantiation of the log-local principle of van Garrel-Graber-Ruddat in the non-compact setting. Our correspondences are based on localization. We also discuss generalizations and implications of our correspondences. Joint work with Chiu-Chu Melissa Liu.