2023 Theses Doctoral

# Open/closed correspondence and mirror symmetry

We develop the mathematical theory of the open/closed correspondence, proposed by Mayr in physics as a class of dualities between open strings on Calabi-Yau 3-folds and closed strings on Calabi-Yau 4-folds. Given an open geometry on a toric Calabi-Yau 3-orbifold relative to a framed Aganagic-Vafa outer brane, we construct a closed geometry on a toric Calabi-Yau 4-orbifold and establish the correspondence between the two geometries on the following levels across both the A- and B-sides of mirror symmetry: numerical Gromov-Witten invariants; generating functions of Gromov-Witten invariants; B-model hypergeometric functions and Givental-style mirror theorems; Picard-Fuchs systems and solutions; integral cycles on Hori-Vafa mirrors and periods; mixed Hodge structures.

## Subjects

## Files

- Yu_columbia_0054D_17776.pdf application/pdf 1.2 MB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Liu, Chiu-Chu
- Degree
- Ph.D., Columbia University
- Published Here
- May 3, 2023