Hodge-GUE correspondence and the discrete KdV equation

DOI10.1007/s00220-020-03846-6zbMath1455.37056arXiv1612.02333OpenAlexW3086463376MaRDI QIDQ2006397

Si-Qi Liu, Di Yang, You-Jin Zhang, B. A. Dubrovin

Publication date: 9 October 2020

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

Full work available at URL: https://arxiv.org/abs/1612.02333

zbMATH Keywords

tau functionHodge integralsdiscrete KdV hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Hodge theory in global analysis (58A14) Lattice dynamics; integrable lattice equations (37K60) Integrable difference and lattice equations; integrability tests (39A36)

Related Items

The loop equation for special cubic Hodge integrals, DYNAMICAL BEHAVIOR OF THE LONG WAVES IN THE NONLINEAR DISPERSIVE MEDIA THROUGH ANALYTICAL AND NUMERICAL INVESTIGATION, On a new proof of the Okuyama–Sakai conjecture, GUE via Frobenius manifolds. I: From matrix gravity to topological gravity and back, From wave functions to tau-functions for the Volterra lattice hierarchy, Fractional Volterra hierarchy, Simple maps, Hurwitz numbers, and topological recursion, The Hodge-FVH correspondence, Jacobi ensemble, Hurwitz numbers and Wilson polynomials, On equivariant Gromov-Witten invariants of resolved conifold with diagonal and anti-diagonal actions, Grothendieck’s dessins d’enfants in a web of dualities. III

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
• Remodeling the B-model
• Topological open strings on orbifolds
• A mathematical theory of the topological vertex
• Quantum field theory techniques in graphical enumeration
• Intersection theory on the moduli space of curves and the matrix Airy function
• Localization of virtual classes
• Graphs on surfaces and their applications. Appendix by Don B. Zagier
• Generating series for GUE correlators
• Fractional Volterra hierarchy
• On cubic Hodge integrals and random matrices
• Virasoro symmetries of the extended Toda hierarchy
• The Euler characteristic of the moduli space of curves
• Planar diagrams
• A proof of a conjecture of Mariño-Vafa on Hodge integrals
• Hodge integrals and Gromov-Witten theory
• Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture
• The topological vertex
• Integrals over classical groups, random permutations, Toda and Toeplitz lattices
• Integrability and matrix models
• A formula of two-partition Hodge integrals
• Hamiltonian Perturbations of Hyperbolic PDEs: from Classification Results to the Properties of Solutions
• On the remodeling conjecture for toric Calabi-Yau 3-orbifolds
• On the gauge theory/geometry correspondence
• An asymptotic expansion of the double gamma function