Weighted Hurwitz numbers and topological recursion: An overview

DOI10.1063/1.5013201zbMath1401.14147arXiv1610.09408OpenAlexW2949376609WikidataQ58009607 ScholiaQ58009607MaRDI QIDQ4586466

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Publication date: 13 September 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.09408

zbMATH Keywords

Hurwitz numberspectral curveBaker functionChristoffel-Darboux relationhypergeometric \(\tau\)-functions

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Compact Riemann surfaces and uniformization (30F10) Other hypergeometric functions and integrals in several variables (33C70) Relationships between surfaces, higher-dimensional varieties, and physics (14J81) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Coverings of curves, fundamental group (14H30) Generalized hypergeometric series, ({}_pF_q) (33C20) Low-dimensional topology of special (e.g., branched) coverings (57M12)

Related Items (20)

Cut-and-join equation for monotone Hurwitz numbers revisited ⋮ Analyticity of the free energy for quantum Airy structures ⋮ Explicit closed algebraic formulas for Orlov-Scherbin \(n\)-point functions ⋮ Fermionic approach to weighted Hurwitz numbers and topological recursion ⋮ Bi-pruned Hurwitz numbers ⋮ Topological recursion for monotone orbifold Hurwitz numbers: a proof of the Do-Karev conjecture ⋮ Generating functions for weighted Hurwitz numbers ⋮ Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewański conjecture ⋮ Whittaker vectors for \(\mathcal{W}\)-algebras from topological recursion ⋮ 2D Yang–Mills Theory and Tau Functions ⋮ Weighted Hurwitz numbers and topological recursion ⋮ A monodromy graph approach to the piecewise polynomiality of simple, monotone and Grothendieck dessins d'enfants double Hurwitz numbers ⋮ Constellations and \(\tau\)-functions for rationally weighted Hurwitz numbers ⋮ Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and double simple Hurwitz numbers ⋮ Rationally weighted Hurwitz numbers, Meijer G-functions and matrix integrals ⋮ Generating weighted Hurwitz numbers ⋮ Degrees in random uniform minimal factorizations ⋮ Weighted Hurwitz Numbers, "Equation missing" -Functions, and Matrix Integrals ⋮ Random generation and scaling limits of fixed genus factorizations into transpositions ⋮ Matrix model generating function for quantum weighted Hurwitz numbers

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