Ramifications of Hurwitz theory, KP integrability and quantum curves

Abstract

In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves from the point of view of KP integrability and derive new examples of quantum curves for the families of double Hurwitz numbers.

30 pages, references updated, minor corrections

References in corpus (5)

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• Fermionic approach to weighted Hurwitz numbers and topological recursion
• Simple maps, Hurwitz numbers, and Topological Recursion
• On W-operators and superintegrability for dessins d'enfant
• Towards an orbifold generalization of Zvonkine's $r$-ELSV formula
• Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
• Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
• Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals
• Cut-and-join equation for monotone Hurwitz numbers revisited
• Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion
• Relations on ${\overline{\mathcal{M}}}_{g,n}$ and the negative $r$-spin Witten conjecture
• KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model
• Higher genera Catalan numbers and Hirota equations for extended nonlinear Schroedinger hierarchy
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III
• Symplectic duality for topological recursion
• Generalized $\tilde{W}$ algebras
• Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers
• 4D limit of melting crystal model and its integrable structure
• Completed Cycles Leaky Hurwitz Numbers