Orbifold Hurwitz numbers and Eynard-Orantin invariants

Abstract

We prove that a generalisation of simple Hurwitz numbers due to Johnson, Pandharipande and Tseng satisfy the topological recursion of Eynard and Orantin. This generalises the Bouchard-Marino conjecture and places Hurwitz-Hodge integrals, which arise in the Gromov--Witten theory of target curves with orbifold structure, in the context of the Eynard-Orantin topological recursion.

29 pages

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• Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
• Loop equations and a proof of Zvonkine's $qr$-ELSV formula
• Topological recursion and a quantum curve for monotone Hurwitz numbers
• Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson-Pandharipande-Tseng formula
• Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
• Towards an orbifold generalization of Zvonkine's $r$-ELSV formula
• Super Quantum Airy Structures
• Quantizing Weierstrass
• Special cases of the orbifold version of Zvonkine's $r$-ELSV formula
• Log topological recursion through the prism of $x-y$ swap
• An intersection-theoretic proof of the Harer-Zagier formula
• On the Goulden-Jackson-Vakil conjecture for double Hurwitz numbers
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• Pruned Hurwitz numbers
• Airy structures for semisimple Lie algebras
• Integration on complex Grassmannians, deformed monotone Hurwitz numbers, and interlacing phenomena
• Triply mixed coverings of arbitrary base curves: Quasimodularity, quantum curves and a mysterious topological recursions
• Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers
• Local topological recursion governs the enumeration of lattice points in ${\overline{\mathcal{M}}}_{g,n}$
• $\mathfrak{b}$-Hurwitz numbers from refined topological recursion
• Generalisations of the Harer-Zagier recursion for 1-point functions
• Counting curves on surfaces