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

  title={Extended r-spin theory in all genera and the discrete KdV hierarchy},
  author={Alexandr Buryak and Paolo Rossi},
  journal={Advances in Mathematics},

Quadratic double ramification integrals and the noncommutative KdV hierarchy

In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of

Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies

We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat

Semisimple Flat F-Manifolds in Higher Genus

In this paper, we generalize the Givental theory for Frobenius manifolds and cohomological field theories to flat F-manifolds and F-cohomological field theories. In particular, we define a notion of

Moduli spaces of residueless meromorphic differentials and the KP hierarchy

We prove that the cohomology classes of the moduli spaces of residueless meromorphic differentials, i.e., the closures, in the moduli space of stable curves, of the loci of smooth curves whose marked

Tautological relations and integrable systems

. We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus g with n marked points. A large part of these relations has a

Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics

In this paper, we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold, we present a construction of a canonical flat

Extended lattice Gelfand–Dickey hierarchy

  • K. Takasaki
  • Computer Science, Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
This work proposes an extension of the lattice GD hierarchy that has an infinite number of logarithmic flows alongside the usual flows and presents the Lax, Sato and Hirota equations and a factorization problem of difference operators that captures the whole set of solutions.

Riemann-Hilbert-Birkhoff inverse problem for semisimple flat $F$-manifolds, and convergence of oriented associativity potentials

In this paper, we address the problem of classification of quasi-homogeneous formal power series providing solutions of the oriented associativity equations. Such a classification is performed by



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

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