Explore the mathematical formulation of the open/closed correspondence in genus zero between open Gromov-Witten theory of toric Calabi-Yau 3-folds and closed Gromov-Witten theory of toric Calabi-Yau 4-folds in this 52-minute lecture by Song Yu from Columbia University. Delve into the correspondence at both numerical and generating function levels, examining its compatibility with open and closed mirror symmetry. Learn about noncompact manifolds, synthetic quotients, Lagrangians, relative geometry, and the loglocal principle. Gain insights into potential applications and follow the roadmap from introduction to conclusion, covering key concepts such as open/closed correspondence levels, construction methods, and proofs.