Double ramification cycles and integrable hierarchies

DOI10.1007/s00220-014-2235-2zbMath1329.14103arXiv1403.1719OpenAlexW2088578613WikidataQ59897042 ScholiaQ59897042MaRDI QIDQ2018315

Yanyan Li

Publication date: 14 April 2015

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

Full work available at URL: https://arxiv.org/abs/1403.1719

zbMATH Keywords

integrable systemGromov-Witten invariantshierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35)

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Cites Work

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• Gromov-Witten theory of Fano orbifold curves, gamma integral structures and ADE-Toda hierarchies
• The Witten equation, mirror symmetry, and quantum singularity theory
• On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket
• Polynomial families of tautological classes on \(\mathcal M^{\mathrm{rt}}_{g,n}\)
• Dubrovin-Zhang hierarchy for the Hodge integrals
• Rational reductions of the 2D-Toda hierarchy and mirror symmetry
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary
• Relative virtual localization and vanishing of tautological classes of moduli spaces of curves
• KP hierarchy for Hodge integrals
• Intersection theory on the moduli space of curves and the matrix Airy function
• Relative maps and tautological classes
• Virasoro symmetries of the extended Toda hierarchy
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• A polynomial bracket for the Dubrovin-Zhang hierarchies
• Integrable hierarchies and the mirror model of local \({\mathbb {CP}}^{1}\)
• The equivariant Gromov-Witten theory of \(\mathbb P^1\)
• Open intersection numbers and the wave function of the KdV hierarchy
• Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of $\mathbb {C}P^1$ orbifolds
• The double ramification cycle and the theta divisor
• Normal Functions and the Geometry of Moduli Spaces of Curves
• Gromov–Witten invariants and integrable hierarchies of topological type
• String, Dilaton, and Divisor Equation in Symplectic Field Theory
• Tautological relations and the $r$-spin Witten conjecture
• Geometry of Algebraic Curves
• The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies
• BCOV theory via Givental group action on cohomological field theories
• Integrable systems and holomorphic curves
• Integrals of $\psi$-classes over double ramification cycles
• New moduli spaces of pointed curves and pencils of flat connections.