From topological recursion to wave functions and PDEs quantizing hyperelliptic curves

DOI10.1017/fms.2023.96zbMath1524.14076arXiv1911.07795OpenAlexW2984082977MaRDI QIDQ6087247

Elba Garcia-Failde, Bertrand Eynard

Publication date: 15 November 2023

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.07795

zbMATH Keywords

topological recursionWKB solutionquantum curve

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Schrödinger operator, Schrödinger equation (35J10) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Relationships between algebraic curves and integrable systems (14H70) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (3)

Whittaker vectors for \(\mathcal{W}\)-algebras from topological recursion ⋮ Quantization of Calogero-Painlevé system and multi-particle quantum Painlevé equations II-VI ⋮ Topological recursion and uncoupled BPS structures. I: BPS spectrum and free energies

Cites Work

• Geometry of spectral curves and all order dispersive integrable system
• A holomorphic and background independent partition function for matrix models and topological strings
• The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
• Hermitian matrix model free energy: Feynman graph technique for all genera
• Free energy topological expansion for the 2-matrix model
• Matrix eigenvalue model: Feynman graph technique for all genera
• Rational differential systems, loop equations, and application to the \(q\)th reductions of KP
• Quantum curve and the first Painlevé equation
• Counting surfaces. CRM Aisenstadt chair lectures
• 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
• Invariants of algebraic curves and topological expansion
• Quantizing Weierstrass
• Reconstructing WKB from topological recursion
• Painlevé equations, topological type property and reconstruction by the topological recursion
• 2-parameter \(\tau\)-function for the first Painlevé equation: topological recursion and direct monodromy problem via exact WKB analysis
• All order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials
• Abstract loop equations, topological recursion and new applications
• The volume conjecture and topological strings
• Mixed correlation function and spectral curve for the 2-matrix model
• Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: The sl2 case
• Blobbed topological recursion: properties and applications

This page was built for publication: From topological recursion to wave functions and PDEs quantizing hyperelliptic curves