DR hierarchies: from the moduli spaces of curves to integrable systems

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Families, moduli of curves (algebraic) (14H10)

Cites Work

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Double ramification cycles and quantum integrable systems
Recursion relations for double ramification hierarchies
Towards a description of the double ramification hierarchy for Witten's $r$-spin class
The Witten equation, mirror symmetry, and quantum singularity theory
The structure of 2D semi-simple field theories
Dubrovin-Zhang hierarchy for the Hodge integrals
Relative virtual localization and vanishing of tautological classes of moduli spaces of curves
Towards a bihamiltonian structure for the double ramification hierarchy
The virtual class of the moduli stack of stable $r$-spin curves
A construction of the Deligne-Mumford orbifold
Intersection theory on algebraic stacks and on their moduli spaces
Intersection theory on the moduli space of curves and the matrix Airy function
Integrable structure of conformal field theory. II: $Q$-operator and DDV equation
Integrable structure of conformal field theory. III: The Yang-Baxter relation
Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation
Gromov-Witten invariants in algebraic geometry
Relative maps and tautological classes
Virasoro symmetries of the extended Toda hierarchy
Stacks of stable maps and Gromov-Witten invariants
Gromov-Witten classes, quantum cohomology, and enumerative geometry
Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
A polynomial bracket for the Dubrovin-Zhang hierarchies
Hodge integrals and Gromov-Witten theory
Invertible cohomological field theories and Weil-Petersson volumes
Tau-structure for the double ramification hierarchies
Double ramification cycles and integrable hierarchies
The bi-Hamiltonian structures of the DR and DZ hierarchies in the approximation up to genus one
Zero modes of local operators in 2d CFT on a cylinder
Flat F-manifolds, F-CohFTs, and integrable hierarchies
DR/DZ equivalence conjecture and tautological relations
Witten's top Chern class via cosection localization
Double ramification cycles on the moduli spaces of curves
The equivariant Gromov-Witten theory of $\mathbb P^1$
The irreducibility of the space of curves of a given genus
The double ramification cycle and the theta divisor
Normal Functions and the Geometry of Moduli Spaces of Curves
Tautological relations and the $r$-spin Witten conjecture
Weil-Petersson volumes and intersection theory on the moduli space of curves
The Witten top Chern class via 𝐾-theory
An algebro-geometric proof of Witten’s conjecture
A simple model of the integrable Hamiltonian equation
Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
Cellular decompositions of compactified moduli spaces of pointed curves
Buryak–Okounkov Formula for the n-Point Function and a New Proof of the Witten Conjecture
A calculus for the moduli space of curves
Integrals of $\psi$-classes over double ramification cycles
Relations on \overline{ℳ}_{ℊ,𝓃} via 3-spin structures
A GENERALISATION OF WITTEN’S CONJECTURE FOR THE PIXTON CLASS AND THE NONCOMMUTATIVE KDV HIERARCHY

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