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arXiv · 1307.4729

Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula

Petr Dunin-Barkowski·Maxim Kazarian·Nicolas Orantin·Sergey Shadrin·Loek Spitz
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Abstract

In this paper we give a new proof of the ELSV formula. First, we refine an argument of Okounkov and Pandharipande in order to prove (quasi-)polynomiality of Hurwitz numbers without using the ELSV formula (the only way to do that before used the ELSV formula). Then, using this polynomiality we give a new proof of the Bouchard-Mariño conjecture. After that, using the correspondence between the Givental group action and the topological recursion coming from matrix models, we prove the equivalence of the Bouchard-Mariño conjecture and the ELSV formula (it is a refinement of an argument by Eynard).

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Petr Dunin-Barkowski, Maxim Kazarian, Nicolas Orantin, Sergey Shadrin, Loek Spitz. 2013-12-31. Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula. https://doi.org/10.1016/j.aim.2015.03.016

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