# Mariño-Vafa formula and Hodge integral identities

@article{Liu2003MarioVafaFA, title={Mari{\~n}o-Vafa formula and Hodge integral identities}, author={Chiu-Chu Melissa Liu and Kefeng Liu and Jian Zhou}, journal={Journal of Algebraic Geometry}, year={2003}, volume={15}, pages={379-398} }

Based on string duality Marino and Vafa [10] conjectured a closed formula on certain Hodge integrals in terms of representations of symmetric groups. This formula was first explicitly written down by the third author in [13] and proved in joint work [8] of the authors of the present paper. For a different approach see [12]. Our proof follows the strategy of proving both sides of the equation satisfy the same cut-and-join equation and have the same initial values. In this note we will describe a…

## 42 Citations

SOME RESULTS OF THE MARIÑO-VAFA FORMULA

- Mathematics
- 2006

In this paper we derive some new Hodge integral identities by taking the limits of Mariño-Vafa formula. These identities include the formula of λ1λg-integral on Mg,1, the vanishing result of…

Some Results of the Mari˜no -vafa Formula

- Mathematics
- 2006

Abstract. In this paper we derive some new Hodge integral identities by taking the limits of Mariño-Vafa formula. These identities include the formula of λ1λg-integral on Mg,1, the vanishing result…

Some Results of the Mari˜no -vafa Formula

- Mathematics
- 2006

In this paper we derive some new Hodge integral identities by taking limits of the Mariño-Vafa formula. These identities include the formula of λ 1 λ g-integral on M g,1 , the vanishing result of λ g…

Hodge integrals and invariants of the unknot

- Mathematics
- 2004

We prove the Gopakumar{Mari~ no{Vafa formula for special cubic Hodge integrals. The GMV formula arises from Chern{Simons/string duality applied to the unknot in the three sphere. The GMV formula is a…

Some results of Marino-Vafa formula

- Mathematics
- 2006

In this paper we derive some new Hodge integral identities by taking limits of the Marino-Vafa formula. These identities include the formula of lambda_{1}lambda_{g}-integral on M_{g,1}, the vanishing…

SOME RESULTS OF THE MARIÑO-VAFA FORMULA

- Mathematics
- 2006

In this paper we derive some new Hodge integral identities by taking limits of the Mariño-Vafa formula. These identities include the formula of λ 1 λ g-integral on M g,1 , the vanishing result of λ g…

Hodge integrals, Hurwitz numbers, and Symmetric Groups

- Mathematics
- 2003

We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the…

Hurwitz numbers, matrix models and enumerative geometry

- Mathematics
- 2007

We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric…

On explicit formulae of LMOV invariants

- MathematicsJournal of High Energy Physics
- 2019

Abstract
We started a program to study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane) several years ago. This paper is…

0 Se p 20 07 Hurwitz numbers , matrix models and enumerative geometry

- Mathematics
- 2008

We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric…

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Hodge integrals and invariants of the unknot

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We prove the Gopakumar{Mari~ no{Vafa formula for special cubic Hodge integrals. The GMV formula arises from Chern{Simons/string duality applied to the unknot in the three sphere. The GMV formula is a…

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