Tau-functions and monodromy symplectomorphisms

DOI10.1007/s00220-021-04224-6OpenAlexW3207914960MaRDI QIDQ2244086

Marco Bertola, Dmitry Korotkin

Publication date: 11 November 2021

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

Full work available at URL: https://arxiv.org/abs/1910.03370

zbMATH Keywords

Hamiltonian formulationmonodromy mapSchlesinger equations\(r\)-matrix structure

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) Momentum maps; symplectic reduction (53D20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Canonical transformations in symplectic and contact geometry (53D22) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06) Symplectic and canonical mappings (37J11)

Related Items

On the tau function of the hypergeometric equation ⋮ Isomonodromic deformations: confluence, reduction and quantisation ⋮ Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus ⋮ On generalized WKB expansion of monodromy generating function ⋮ Extended Goldman symplectic structure in Fock-Goncharov coordinates ⋮ Szegő kernel and symplectic aspects of spectral transform for extended spaces of rational matrices ⋮ Generating Function of Monodromy Symplectomorphism for 2 × 2 Fuchsian Systems and Its WKB Expansion ⋮ Enumerative geometry of surfaces. Abstracts from the workshop held June 13--19, 2021 (hybrid meeting) ⋮ Perturbative connection formulas for Heun equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The dependence on the monodromy data of the isomonodromic tau function
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Quasi-Hamiltonian geometry of meromorphic connections
• The symplectic nature of fundamental groups of surfaces
• Invariant functions on Lie groups and Hamiltonian flows of surface group representations
• Holonomic quantum fields. II: The Riemann-Hilbert problem
• \((T^*G)_ t\): a toy model for conformal field theory
• Quantization of coset space \(\sigma\)-models coupled to two-dimensional gravity
• Extended moduli spaces of flat connections on Riemann surfaces
• Monodromy dependence and connection formulae for isomonodromic tau functions
• Symplectic geometry of the moduli space of projective structures in homological coordinates
• Rogers dilogarithms of higher degree and generalized cluster algebras
• Torus actions on symplectic manifolds
• Symplectic structure of the moduli space of flat connection on a Riemann surface
• The symplectic nature of the space of projective connections on Riemann surfaces
• The hyperbolic moduli space of flat connections and the isomorphism of symplectic multiplicity spaces
• WKB expansion for a Yang-Yang generating function and the Bergman tau function
• Moduli spaces of local systems and higher Teichmüller theory
• Correction to: ``The dependence on the monodromy data of the isomonodromic tau function
• On dynamicalr-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras
• Shear coordinate description of the quantized versal unfolding of aD₄singularity
• Introduction to Classical Integrable Systems
• Connection Problem for the Tau-Function of the Sine-Gordon Reduction of Painlevé-III Equation via the Riemann-Hilbert Approach
• On Some Hamiltonian Properties of the Isomonodromic Tau Functions
• Painlevé Monodromy Manifolds, Decorated Character Varieties, and Cluster Algebras
• A symplectic groupoid of triangular bilinear forms and the braid group
• Periods of meromorphic quadratic differentials and Goldman bracket
• A quantum Teichmüller space

This page was built for publication: Tau-functions and monodromy symplectomorphisms