Quantization of spectral curves for meromorphic Higgs bundles through topological recursion

DOI10.1090/pspum/100/01780zbMath1452.14031arXiv1411.1023OpenAlexW2963169492MaRDI QIDQ5136635

Olivia Dumitrescu, Motohico Mulase

Publication date: 27 November 2020

Published in: Proceedings of Symposia in Pure Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.1023

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Topological field theories in quantum mechanics (81T45) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Relationships between algebraic curves and physics (14H81) Families, moduli of curves (analytic) (14H15) Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category (53D37) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (6)

Index of rigidity of differential equations and Euler characteristic of their spectral curves ⋮ Integrable differential systems of topological type and reconstruction by the topological recursion ⋮ Loop equations from differential systems on curves ⋮ Whittaker vectors for \(\mathcal{W}\)-algebras from topological recursion ⋮ A journey from the Hitchin section to the oper moduli ⋮ Airy structures and symplectic geometry of topological recursion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral curves and the Schrödinger equations for the Eynard-Orantin recursion
• Think globally, compute locally
• The spectral curve and the Schrödinger equation of double Hurwitz numbers and higher spin structures
• Topological recursion for the Poincaré polynomial of the combinatorial moduli space of curves
• Quantum spectral curve for the Gromov-Witten theory of the complex projective line
• Polynomial recursion formula for linear Hodge integrals
• The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
• The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers
• Stable bundles and integrable systems
• On the centralizer of diffeomorphisms of the half-line
• Free energy topological expansion for the 2-matrix model
• Topological strings and integrable hierarchies
• Remodeling the B-model
• Models of discretized moduli spaces, cohomological field theories, and Gaussian means
• Axiomatic quantum field theory in terms of operator product expansions: general framework, and perturbation theory via Hochschild cohomology
• Topological open strings on orbifolds
• Electric-magnetic duality and the geometric Langlands program
• Invariants of algebraic curves and topological expansion
• Intersection theory on the moduli space of curves and the matrix Airy function
• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Interplay between opers, quantum curves, WKB analysis, and Higgs bundles
• A-polynomial, B-model, and quantization
• Quantum curves for the enumeration of ribbon graphs and hypermaps
• The colored Jones function is \(q\)-holonomic
• Mirror symmetry for orbifold Hurwitz numbers
• Counting rooted maps by genus. I
• On \(\lambda\)-connections on a curve where \(\lambda\) is a formal parameter
• Mirror Symmetry, Hitchin's Equations, And Langlands Duality
• Hitchin integrable systems, deformations of spectral curves, and KP-type equations
• D-Branes and D-Modules
• The Self-Duality Equations on a Riemann Surface
• Stable pairs on curves and surfaces
• Wild non-abelian Hodge theory on curves
• Wall-Crossing Structures in Donaldson–Thomas Invariants, Integrable Systems and Mirror Symmetry
• The spectral curve of the Eynard-Orantin recursion via the Laplace transform
• GAUGE THEORY AND WILD RAMIFICATION
• Quantization and unitary representations
• Symplectic manifolds and isomonodromic deformations

This page was built for publication: Quantization of spectral curves for meromorphic Higgs bundles through topological recursion