KP hierarchy for Hodge integrals

By M. Kazarian. 2008

138 citations recorded by the source corpus.

Abstract Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's λ g -conjecture, etc. Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8835a4f88a53b19556ba2f3971e91de2e39909e2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. B. Eynard
2. Brad Safnuk
3. M. Mulase
4. A. Mironov
5. A. Morozov
6. A. Alexandrov
7. Naizhen Zhang
8. Ian P. Goulden

In Geometry and Topology

1. Guillaume Chapuy
2. J. Harnad
3. A. Alexandrov
4. A. Morozov
5. M. Mulase
6. A. Mironov
7. Naizhen Zhang
8. Brad Safnuk

In Mathematical Physics

1. B. Eynard
2. Brad Safnuk
3. A. Alexandrov
4. Guillaume Chapuy
5. J. Harnad
6. M. Mulase
7. A. Morozov
8. A. Mironov

Citations in the corpus

• Polynomiality of monotone Hurwitz numbers in higher genera (2012, unknown): “[13] M. E. Kazarian and S. K. Lando, An algebro-geometric proof of Witten’s conjecture, J. Amer.”
• Polynomial recursion formula for linear Hodge integrals (2009, methodology): “lation of the cut-and-join equation (3.14) and a new point of view of understanding (1.2) as the Laplace transform of (3.14). It gives a clear and unified picture of some of the results established in [4, 16, 20]. The paper is organized as follows. We begin with setting our notations and reviewing de”
• The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers (2009, background): “3, 33]. Among them is a relation to integrable systems such as the Kadomtsev-Petviashvili equations [13]. In recent years these equations have played an essential role in the study of Hurwitz numbers [24, 25, 34, 40, 41, 42]. Since the aim of this paper is to give a proof of the Bouchard-Marino~ con”
• LOCALIZATION IN GROMOV-WITTEN THEORY AND ORBIFOLD GROMOV-WITTEN THEORY (2011, unknown): “[34] M.E. Kazarian, S. K. Lando, “An algebro-geometric proof of Witten’s conjecture,” J. Amer.”
• The KP hierarchy, branched covers, and triangulations (2008, background): “More recently, Kazarian [Ka] has given a number of interesting results about the structure of solutions to the KP hierarchy.”
• Algebra of differential operators associated with Young diagrams (2012, background): “ramewroks: strings and QCD [8], mirror symmetry [7], theory of singularities [1], matrix models [16, 20], integrable systems [26, 14, 25], Yang-Mills theory [6, 14] and the theory of moduli of curves [13, 12, 20] and other branches of string theory. 9 Associate with Young diagrams ∆1,...,∆k and ∆, w”
• 2D Toda τ-Functions as Combinatorial Generating Functions (2015, unknown): “These include the Kontsevich matrix integral [22], which is a KdV τ -function, the generator for Hodge invariants [21], the matrix integrals that generate single Hurwitz numbers [3] [25], and the ones for Belyi curves and dessins d'enfants [2].”
• Weighted Hurwitz Numbers and Topological Recursion (2018, background): “There has also been important progress in relating Hurwitz numbers to other classes of enumerative geometric invariants [2, 21,26,33,40,55,65,68,69,72] and matrix models [1, 6–9,17,21,25,61,64,68,69].”