Geometry and arithmetic of integrable hierarchies of KdV type. I: Integrality

DOI10.1016/j.aim.2023.109311zbMath1524.14075arXiv2101.10924OpenAlexW4387387529MaRDI QIDQ6058886

Di Yang, Don Zagier, B. A. Dubrovin

Publication date: 1 November 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.10924

zbMATH Keywords

integrable systemwave functionintegralityFJRW invariantstopological ODEs

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Families, moduli of curves (algebraic) (14H10) 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) Geometric quantization (53D50) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45)

Related Items

On the large genus asymptotics of psi-class intersection numbers

Cites Work

• New results of intersection numbers on moduli spaces of curves
• Vertices from replica in a random matrix theory
• Relations on \overline{ℳ}_{ℊ,𝓃} via 3-spin structures
• Extended $r$-spin theory and the mirror symmetry for the $A_{r-1}$-singularity
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
• Witten's \(D_4\) integrable hierarchies conjecture
• The Witten equation, mirror symmetry, and quantum singularity theory
• Topological recursions of Eynard-Orantin type for intersection numbers on moduli spaces of curves
• Uniqueness theorem of \(\mathcal W\)-constraints for simple singularities
• Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
• Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi
• The structure of 2D semi-simple field theories
• BCFG Drinfeld-Sokolov hierarchies and FJRW-theory
• Differential equations in the spectral parameter
• Soliton equations, vertex operators, and simple singularities
• Period mapping associated to a primitive form
• The virtual class of the moduli stack of stable \(r\)-spin curves
• Stable twisted curves and their \(r\)-spin structures
• Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures
• Loop groups and equations of KdV type
• Perturbative series and the moduli space of Riemann surfaces
• On the structure of Brieskorn lattice
• Intersection theory on the moduli space of curves and the matrix Airy function
• A matrix integral solution to two-dimensional \(W_ p\)-gravity
• Periodic problems for the Korteweg-de Vries equation in the class of finite band potentials
• Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
• Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation
• Integrable hierarchy underlying topological Landau-Ginzburg models of \(D\)-type
• On a linear structure of the quotient variety by a finite reflexion group
• A new description of the \(E_6\) singularity
• The arithmetic and topology of differential equations
• Reconstructing WKB from topological recursion
• The Euler characteristic of the moduli space of curves
• Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities
• Poisson-Lie group of pseudodifferential symbols
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• A polynomial bracket for the Dubrovin-Zhang hierarchies
• The \(n\)-point functions for intersection numbers on moduli spaces of curves
• Extended affine Weyl groups of BCD-type: their Frobenius manifolds and Landau-Ginzburg superpotentials
• Borodin-Okounkov formula, string equation and topological solutions of Drinfeld-Sokolov hierarchies
• Punctures and \(p\)-spin curves from matrix models. II
• Matrix model for the total descendant potential of a simple singularity of type \(D\)
• Punctures and \(p\)-spin curves from matrix models. III: \(D_l\) type and logarithmic potential
• Toda theory and \({\mathcal W}\)-algebra from a gauged WZNW point of view
• Gromov-Witten invariants of the Riemann sphere
• Witten's top Chern class via cosection localization
• Formal pseudodifferential operators and Witten's \(r\)-spin numbers
• Geometric interpretation of Zhou's explicit formula for the Witten-Kontsevich tau function
• Correlation functions of the KdV hierarchy and applications to intersection numbers over \(\overline{\mathcal{M}}_{g, n}\)
• The irreducibility of the space of curves of a given genus
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case
• Closed extended \(r\)-spin theory and the Gelfand-Dickey wave function
• On tau-functions for the KdV hierarchy
• TOPOLOGICAL FIELD THEORIES AND THE PERIOD INTEGRALS
• ON DUBROVIN TOPOLOGICAL FIELD THEORIES
• Open intersection numbers and the wave function of the KdV hierarchy
• Random Matrix Theory with an External Source
• Gromov–Witten invariants and integrable hierarchies of topological type
• On the Drinfeld-Sokolov Hierarchies of D Type
• Quantization of soliton systems and Langlands duality
• Tautological relations and the $r$-spin Witten conjecture
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• A remark on Kac–Wakimoto hierarchies of D-type
• The Witten top Chern class via 𝐾-theory
• MATRIX AIRY FUNCTIONS FOR COMPACT LIE GROUPS
• Introduction to Classical Integrable Systems
• CORRELATION FUNCTIONS FOR TOPOLOGICAL LANDAU-GINZBURG MODELS WITH c≤3
• Simple Lie Algebras and Topological ODEs
• DUBROVIN’S SUPERPOTENTIAL AS A GLOBAL SPECTRAL CURVE
• ON THE GENUS EXPANSION IN THE TOPOLOGICAL STRING THEORY
• Open Saito Theory for A and D Singularities
• E8 spectral curves
• Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions
• -constraints for the total descendant potential of a simple singularity
• Double ramification cycles and the $n$-point function for the moduli space of curves
• Tautological relations via 𝑟-spin structures