2013/07/31 by Petr Dunin-Barkowski, Petr Dunin‐Barkowski, Maxim Kazarian +4 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Argument (complex analysis) #Combinatorics #Conjecture #Equivalence (formal languages) #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Recursion (computer science) #hep-th #math-ph #math.AG #math.MP
paper · pdf · doi:10.1016/j.aim.2015.03.016
published as Advances in Mathematics, Volume 279, Pages 67-103 (2015) · 26 pages; minor inconsistency corrected, references added
arxiv created 2013/12/31 · openalex publication_date 2015/04/18 · arxiv updated 2015/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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).