Weighted Hurwitz Numbers, "Equation missing" -Functions, and Matrix Integrals

DOI10.1007/978-3-030-55777-5_7zbMath1483.14059arXiv2002.07935OpenAlexW3007646358MaRDI QIDQ5011779

J. Harnad

Publication date: 27 August 2021

Published in: Quantum Theory and Symmetries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.07935

zbMATH Keywords

\(\tau\)-functionsHurwitz numbers

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Other functions coming from differential, difference and integral equations (33E30) Coverings of curves, fundamental group (14H30) Generalized hypergeometric series, ({}_pF_q) (33C20) Relationships between algebraic curves and physics (14H81)

Cites Work

• Toda equations for Hurwitz numbers
• 2D Toda \(\tau\)-functions as combinatorial generating functions
• Hypergeometric \(\tau\)-functions, Hurwitz numbers and enumeration of paths
• Gromov-Witten theory, Hurwitz theory, and completed cycles
• Weighted Hurwitz numbers and hypergeometric $\tau$-functions: an overview
• Weighted Hurwitz numbers and topological recursion: An overview
• Rationally weighted Hurwitz numbers, Meijer G-functions and matrix integrals
• Generating weighted Hurwitz numbers
• Generating functions for weighted Hurwitz numbers

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