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].

22 pages. Version 4: improved exposition of the proof

References in corpus (3)

• Matrix Models for Random Partitions
• Gromov-Witten invariants of target curves via Symplectic Field Theory
• The Moduli Space of Stables Maps with Divisible Ramification

Cited by in corpus (17)

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• 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
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• 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
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• 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