Combinatorial solutions to integrable hierarchies

DOI10.1070/RM2015v070n03ABEH004952zbMath1330.14061arXiv1512.07172OpenAlexW2179755435MaRDI QIDQ3448652

Maxim E. Kazaryan, Sergei K. Lando

Publication date: 26 October 2015

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.07172

zbMATH Keywords

integrable systemsHurwitz numbersKadomtsev-Petviashvili hierarchyboson-fermion correspondenceToda lattice hierarchy

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Groups and algebras in quantum theory and relations with integrable systems (81R12) Topological quantum field theories (aspects of differential topology) (57R56) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Coverings of curves, fundamental group (14H30)

Related Items (16)

Quantization of Harer-Zagier formulas ⋮ 2D Toda τ functions, weighted Hurwitz numbers and the Cayley graph: Determinant representation and recursion formula ⋮ Explicit formulae for one-part double Hurwitz numbers with completed 3-cycles ⋮ Ramifications of Hurwitz theory, KP integrability and quantum curves ⋮ Explicit closed algebraic formulas for Orlov-Scherbin \(n\)-point functions ⋮ BKP and projective Hurwitz numbers ⋮ Genus expansion of matrix models and \(\hbar\) expansion of KP hierarchy ⋮ Hyperelliptic sigma functions and Adler-Moser polynomials ⋮ Polynomial graph invariants and the KP hierarchy ⋮ Invariants of framed graphs and the Kadomtsev-Petviashvili hierarchy ⋮ Integrals of tau functions: a round dance tau function and multimatrix integrals ⋮ Hurwitz numbers from Feynman diagrams ⋮ Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion ⋮ Rationality in map and hypermap enumeration by genus ⋮ Notes about the KP/BKP correspondence ⋮ Grothendieck’s dessins d’enfants in a web of dualities. III

Cites Work

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• On KP-integrable Hurwitz functions
• Polynomiality of monotone Hurwitz numbers in higher genera
• The matrix model for dessins d'enfants
• Enumeration of chord diagrams on many intervals and their non-orientable analogs
• The KP hierarchy, branched covers, and triangulations
• The map asymptotics constant \(t_{g}\)
• A new construction of Young's seminormal representation of the symmetric groups
• Enumeration of planar constellations
• Toda equations for Hurwitz numbers
• The Toda equations and the Gromov-Witten theory of the Riemann sphere
• Symmetric polynomials and the center of the symmetric group ring
• Invertible cohomological field theories and Weil-Petersson volumes
• 2D Toda \(\tau\)-functions as combinatorial generating functions
• Virasoro constraints and topological recursion for Grothendieck's dessin counting
• Monotone Hurwitz Numbers in Genus Zero
• The Brauer-Manin Obstruction and III[2]
• An algebro-geometric proof of Witten’s conjecture
• COMBINATORICS OF THE MODULAR GROUP II THE KONTSEVICH INTEGRALS
• A New Approach to the Representation Theory of the Symmetric Groups. II
• Multivariate hypergeometric functions as \(\tau\)-functions of Toda lattice and Kadomtsev-Petviashvili equation

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