The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers
By B. Eynard, M. Mulase, Brad Safnuk. 2009
166 citations recorded by the source corpus.
Author(s): Eynard, Bertrand; Mulase, Motohico; Safnuk, Brad | Abstract: We calculate the Laplace transform of the cut-and-join equation of Goulden, Jackson and Vakil. The result is a polynomial equation that has the topological structure identical to the Mirzakhani recursion formula for the Weil-Petersson volume of the moduli space of bordered hyperbolic surfaces. We find that the direct image of this Laplace transformed equation via the inverse of the Lambert W-function is the topological recursion formula for Hurwitz numbers conjectured by Bouchard and Marino using topological string theory.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/605e0dd916c9feb1cf26957844a181ee7b5329ea
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In Algebra and Number Theory
In Applied Mathematics
Citations in the corpus
- Polynomial recursion formula for linear Hodge integrals (2009, methodology): “The number hg,µ of topological types of Hurwitz covers of given genus g and profile µ, counted with the weight factor 1/|Autf |, is the Hurwitz number we are interested in this paper.”
- Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants (2011, background): “REFERENCES [1] Borot, Gaëtan; Eynard, Bertrand; Mulase Motohico and Safnuk, Brad.”
- Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, methodology): “There is another proof of the Bouchard-Mariño conjecture in [17], but it is based on the ELSV formula, so it is not useful for our purposes.”