Abstract: We will discuss a mathematical formulation of the open/closed correspondence originally proposed by Mayr in physics, which is a correspondence in genus zero between the open Gromov-Witten theory of toric Calabi-Yau 3-folds and the closed Gromov-Witten theory of toric Calabi-Yau 4-folds. The correspondence fits into the log-local principle of van Garrel, Graber, and Ruddat which relates log/relative Gromov-Witten theory and local Gromov-Witten theory. We will then report on a recent generalization of the correspondence to the case of multiple Lagrangians on the open side and higher dimensions on the closed side. As an application, we will discuss implications for integrality structures of the Gromov-Witten invariants. This talk is based on joint works with Chiu-Chu Melissa Liu and joint work in progress with Ke Zhang and Zhengyu Zong.