# The Remodeling Conjecture and the Faber–Pandharipande Formula

```@article{Bouchard2011TheRC,
title={The Remodeling Conjecture and the Faber–Pandharipande Formula},
author={Vincent Bouchard and Andrei Catuneanu and Olivier Marchal and Piotr Sułkowski},
journal={Letters in Mathematical Physics},
year={2011},
volume={103},
pages={59-77}
}```
• Published 12 August 2011
• Mathematics
• Letters in Mathematical Physics
In this note, we prove that the free energies Fg constructed from the Eynard–Orantin topological recursion applied to the curve mirror to \$\${\mathbb{C}^3}\$\$ reproduce the Faber–Pandharipande formula for genus g Gromov–Witten invariants of \$\${\mathbb{C}^3}\$\$ . This completes the proof of the remodeling conjecture for \$\${\mathbb{C}^3}\$\$ .
18 Citations
Graph sums in the remodeling conjecture
• Mathematics
Proceedings of Symposia in Pure Mathematics
• 2018
The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau \$3\$-orbifold by Eynard-Orantin's topological recursion
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 \cite{Giv2} \cite{Giv3} \cite{Giv4} to
WKB solutions of difference equations and reconstruction by the topological recursion
The purpose of this article is to analyze the connection between Eynard–Orantin topological recursion and formal WKB solutions of a -difference equation: with . In particular, we extend the notion of
Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Mathematics
• 2013
We present a proof of the mirror conjecture of Aganagic and Vafa (Mirror Symmetry, D-Branes and Counting Holomorphic Discs. http://arxiv.org/abs/hep-th/0012041v1, 2000) and Aganagic et al. (Z
The SYZ mirror symmetry and the BKMP remodeling conjecture
• Mathematics
• 2016
The Remodeling Conjecture proposed by Bouchard-Klemm-Marino-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (open and closed Gromov-Witten invariants) of a
The spectral curve of the Eynard-Orantin recursion via the Laplace transform
• Mathematics
• 2012
The Eynard-Orantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform
Painlevé 2 Equation with Arbitrary Monodromy Parameter, Topological Recursion and Determinantal Formulas
• Mathematics
• 2017
The goal of this article is to prove that the determinantal formulas of the Painlevé 2 system identify with the correlation functions computed from the topological recursion on their spectral curve
On the remodeling conjecture for toric Calabi-Yau 3-orbifolds
• Mathematics
Journal of the American Mathematical Society
• 2019
The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (the all genus open and closed Gromov-Witten invariants)
A Generalized Topological Recursion for Arbitrary Ramification
• Mathematics
• 2014
The Eynard–Orantin topological recursion relies on the geometry of a Riemann surface S and two meromorphic functions x and y on S. To formulate the recursion, one must assume that x has only simple

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