Loop equations and a proof of Zvonkine's $qr$-ELSV formula

Abstract

We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV formula, proposed recently in [KLPS17].

arXiv comment22 pages. Version 4: improved exposition of the proof

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Cited by in corpus (17)

• Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
• Higher Airy structures and topological recursion for singular spectral curves
• Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
• Connection between cut-and-join and Casimir operators
• Log topological recursion through the prism of $x-y$ swap
• Topological Recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots
• On the Goulden-Jackson-Vakil conjecture for double Hurwitz numbers
• Topological recursion for monotone orbifold Hurwitz numbers: a proof of the Do-Karev conjecture
• Symplectic duality for topological recursion
• Generalized $\tilde{W}$ algebras
• The $r$-ELSV Formula via Localisation on the Moduli Space of Stable Maps with Divisible Ramification
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Stable tree expressions with Omega-classes and Double Ramification cycles
• Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers
• Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers
• Local topological recursion governs the enumeration of lattice points in ${\overline{\mathcal{M}}}_{g,n}$
• Any topological recursion on a rational spectral curve is KP integrable