Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$

Abstract

We derive an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed formulæ of a new type for the generating series of intersection numbers of $\psi$-classes as well as of mixed $\psi$- and $\kappa$-classes in full genera.

48 pages including 9 pages of tables; references added. V2: minor corrections in the proof of Theorem 1.2 (statement unaffected)

References in corpus (8)

• Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
• Vertices from replica in a random matrix theory
• Intersection numbers on Deligne-Mumford moduli spaces and quantum Airy curve
• The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy
• Geometric interpretation of Zhou's explicit formula for the Witten-Kontsevich tau function
• Simple Lie algebras and topological ODEs
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs

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• Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
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• On tau-functions for the Toda lattice hierarchy
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• The Kontsevich-Penner matrix integral, isomonodromic tau functions and open intersection numbers
• Topological recursion on the Bessel curve
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• Remarks on intersection numbers and integrable hierarchies. I. Quasi-triviality
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III
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• Buryak-Okounkov formula for the $n$-point function and a new proof of the Witten conjecture
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• Simple Lie algebras and topological ODEs
• Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method
• On an extension of the generalized BGW tau-function
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• On the large genus asymptotics of psi-class intersection numbers
• On tau-functions for the KdV hierarchy
• Fermionic Computations for Integrable Hierarchies
• Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials
• On Gromov--Witten invariants of ${\mathbb{P}}^1$
• A Remark on Equivalence between Two Formulas of the Two point Witten-Kontsevich Correlators
• Gromov--Witten invariants of the Riemann sphere