Polynomiality of Hurwitz numbers,Bouchard–Mariño conjecture,and a new proof of the ELSV formula |
| |
| Authors: | P Dunin-Barkowski M Kazarian N Orantin S Shadrin L Spitz |
| |
| Institution: | 1. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands;2. ITEP, Moscow, Russia;3. Laboratory of Mathematical Physics, National Research University Higher School of Economics, Moscow, Russia;4. Steklov Mathematical Institute, Ul. Gubkina 8, 119991 Moscow, Russia;5. Department of Mathematics, National Research University Higher School of Economics, Moscow, Russia;6. Département de mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland |
| |
| 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). |
| |
| Keywords: | Hurwitz numbers ELSV formula Bouchard&ndash Mariñ o conjecture Semi-infinite wedge formalism Topological recursion Givental group action |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
