Dunin-Barkowski, P.Kazarian, M.Orantin, N.Shadrin, S.Spitz, L.2015-09-282015-09-282015-09-28201510.1016/j.aim.2015.03.016https://infoscience.epfl.ch/handle/20.500.14299/118927WOS:000355358200003In 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-Marino 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-Marino conjecture and the ELSV formula (it is a refinement of an argument by Eynard). (C) 2015 Elsevier Inc. All rights reserved.Hurwitz numbersELSV formulaBouchard-Marino conjectureSemi-infinite wedge formalismTopological recursionGivental group actiontext::journal::journal article::research article