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

@article{Buryak2018ExtendedRT,
  title={Extended r-spin theory in all genera and the discrete KdV hierarchy},
  author={Alexandr Buryak and Paolo Rossi},
  journal={Advances in Mathematics},
  year={2018}
}
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9 Citations
Highly Influential Citations
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Background Citations
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Methods Citations
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9 Citations

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References

SHOWING 1-10 OF 40 REFERENCES

Towards a description of the double ramification hierarchy for Witten's $r$-spin class

Integrable Systems of Double Ramification Type

In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the 1st author, and its quantization. We extend the notion of tau-symmetry to quantum integrable…

New topological recursion relations

Simple boundary expressions for the k-th power of the cotangent line class on the moduli space of stable 1-pointed genus g curves are found for k >= 2g. The method is by virtual localization on the…

Recursion Relations for Double Ramification Hierarchies

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in Buryak (CommunMath Phys 336(3):1085–1107, 2015) using…

Hodge integrals and Gromov-Witten theory

Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these…

Rational reductions of the 2D-Toda hierarchy and mirror symmetry

We introduce and study a two-parameter family of symmetry reductions of the two-dimensional Toda lattice hierarchy, which are characterized by a rational factorization of the Lax operator into a…

Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the…

Flat $F$-manifolds, Miura invariants and integrable systems of conservation laws

We extend some of the results proved for scalar equations in [3,4], to the case of systems of integrable conservation laws. In particular, for such systems we prove that the eigenvalues of a matrix…

Integrable hierarchies and the mirror model of local CP1

The Witten top Chern class via -theory

The Witten top Chern class is the crucial cohomology class needed to state a conjecture by Witten relating the Gelfand–Dikĭı hierarchies to higher spin curves. In [PV01], Polishchuk and Vaintrob…