2015 Theses Doctoral

# Equivariant Gromov-Witten Theory of GKM Orbifolds

In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold X. We generalize the Givental formula which is studied in the smooth case in [41] [42] [43] to the orbifold case. Specifically, we recover the higher genus Gromov-Witten invariants of a GKM orbifold X by its genus zero data. When X is toric, the genus zero Gromov-Witten invariants of X can be explicitly computed by the mirror theorem studied in [22] and our main theorem gives a closed formula for the all genus Gromov-Witten invariants of X. When X is a toric Calabi-Yau 3-orbifold, our formula leads to a proof of the remodeling conjecture in [38]. The remodeling conjecture can be viewed as an all genus mirror symmetry for toric Calabi-Yau 3-orbifolds. In this case, we apply our formula to the A-model higher genus potential and prove the remodeling conjecture by matching it to the B-model higher genus potential.

## Subjects

## Files

- Zong_columbia_0054D_12428.pdf binary/octet-stream 555 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Liu, Chiu-Chu M.
- Degree
- Ph.D., Columbia University
- Published Here
- December 4, 2014