Open/Closed Correspondence and Mirror Symmetry in Gromov-Witten Theory

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.

Introduction
Openclosed correspondence
Levels of correspondence
Roadmap
Noncompact manifold
More examples
X is a synthetic quotient
Lagrangian
Relative Geometry
Construction
First result
Proof
Correspondence
Loglocal principle
Potential applications
Roadmap overview
Generating functions notation
Generating functions equal
Diagram
Conclusion