Publication : t09/101
The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers
Eynard B. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)Mulase M. (UC Davis)
Safnuk B. (Dept. of Mathematics & Statistics McMaster University 1280 Main Street West Hamilton, Ontario Canada L8S 4K1)
Abstract:Année de publication : 2011
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 Mariño using topological string theory.
Revue : Publ. RIMS 47 629-670 (2011)
Preprint : arXiv:0907.5224
Langue : Anglais
