Extended \(r\)-spin theory in all genera and the discrete KdV hierarchy

DOI10.1016/j.aim.2021.107794zbMath1473.14048arXiv1806.09825OpenAlexW3164766109MaRDI QIDQ2039542

Alexandr Buryak, Paolo Rossi

Publication date: 5 July 2021

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

Full work available at URL: https://arxiv.org/abs/1806.09825

zbMATH Keywords

integrable systemsmoduli space of curvesdiscrete KdV hierarchyextended \(r\)-spin classes

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Families, moduli of curves (algebraic) (14H10) Relationships between algebraic curves and integrable systems (14H70) Families, moduli of curves (analytic) (14H15) Higher spin theories (81T11)

Related Items (8)

Extended lattice Gelfand–Dickey hierarchy ⋮ Integrable systems of finite type from F-cohomological field theories without unit ⋮ Integrable hierarchies, Frölicher–Nijenhuis bicomplexes and Lauricella bi-flat F-manifolds ⋮ Riemann–Hilbert–Birkhoff inverse problem for semisimple flat F$F$‐manifolds and convergence of oriented associativity potentials ⋮ Semisimple flat F-manifolds in higher genus ⋮ Flat F-manifolds, F-CohFTs, and integrable hierarchies ⋮ Simple Lax description of the ILW hierarchy ⋮ Quadratic double ramification integrals and the noncommutative KdV hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Recursion relations for double ramification hierarchies
• Towards a description of the double ramification hierarchy for Witten's \(r\)-spin class
• A Landauc-Ginzburg mirror theorem without concavity
• The Witten equation, mirror symmetry, and quantum singularity theory
• BCFG Drinfeld-Sokolov hierarchies and FJRW-theory
• Dubrovin-Zhang hierarchy for the Hodge integrals
• Rational reductions of the 2D-Toda hierarchy and mirror symmetry
• Twisted \(r\)-spin potential and Givental's quantization
• The virtual class of the moduli stack of stable \(r\)-spin curves
• Dressing chains and the spectral theory of the Schrödinger operator
• Hodge integrals in FJRW theory
• Refined open intersection numbers and the Kontsevich-Penner matrix model
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• A polynomial bracket for the Dubrovin-Zhang hierarchies
• Integrable hierarchies and the mirror model of local \({\mathbb {CP}}^{1}\)
• Hodge integrals and Gromov-Witten theory
• Tau-structure for the double ramification hierarchies
• Integrability, quantization and moduli spaces of curves
• Double ramification cycles and integrable hierarchies
• DR/DZ equivalence conjecture and tautological relations
• \(F\)-manifolds with flat structure and Dubrovin's duality
• Closed extended \(r\)-spin theory and the Gelfand-Dickey wave function
• Normal Functions and the Geometry of Moduli Spaces of Curves
• New topological recursion relations
• Tautological relations and the $r$-spin Witten conjecture
• The Witten top Chern class via 𝐾-theory
• Flat F-manifolds, Miura invariants, and integrable systems of conservation laws
• Relations on \overline{ℳ}_{ℊ,𝓃} via 3-spin structures
• Integrable Systems of Double Ramification Type

This page was built for publication: Extended \(r\)-spin theory in all genera and the discrete KdV hierarchy