67 citations · 510 across the 48 of their papers we have counts for
54 papers
Cetraro lectures on integrable systems and moduli spaces of curves
Alexandr Buryak, Paolo Rossi
In these lecture notes we review some constructions and results on the relation between topology of the moduli space of stable curves and integrable systems of evolutionary PDEs.
Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves
Alexandr Buryak, Abner Hernandez Rodriguez
In an earlier paper of P. Rossi and the first author, a construction of a wide class of quantum hierarchies was presented, with the input data given by an arbitrary cohomological f…
Deformations of the Riemann hierarchy and the geometry of
Alexandr Buryak, Paolo Rossi
The Riemann hierarchy is the simplest example of rank one, (+)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the…
Bihamiltonian structure of the DR hierarchy in the semisimple case
Alexandr Buryak, Paolo Rossi
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using th…
Quantum intersection numbers and the Gromov-Witten invariants of
Xavier Blot, Alexandr Buryak
The notion of a quantum tau-function for a natural quantization of the KdV hierarchy was introduced in a work of Dubrovin, Guéré, Rossi, and the second author. A certain natural ch…
An application of the nonlinear reciprocal transformations in the theory of DR hierarchies
Alexandr Buryak, Mikhail Troshkin
We prove that the DR hierarchy corresponding to the family of F-cohomological field theories without unit considered in a previous work of the first author together with D. Gubarev…
Tautological relations and integrable systems
Alexandr Buryak, Sergey Shadrin
We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus with marked points. A large part of the…
A formula for the Gromov-Witten potential of an elliptic curve
Alexandr Buryak
An algorithm to determine all the Gromov-Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants…
A construction of open descendant potentials in all genera
Alexander Alexandrov, Alexey Basalaev, Alexandr Buryak
We present a construction of an open analogue of total descendant and total ancestor potentials via an "open version" of Givental's action. Our construction gives a genus expansion…
Moduli spaces of residueless meromorphic differentials and the KP hierarchy
Alexandr Buryak, Paolo Rossi, Dimitri Zvonkine
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…
A conjectural formula for
Alexandr Buryak, Francisco Hernández Iglesias, Sergey Shadrin
We propose a conjectural formula for and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named…
The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one
Oscar Brauer, Alexandr Buryak
In a recent paper, giving an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space loc…
Riemannian F-manifolds, bi-flat F-manifolds, and flat pencils of metrics
Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni +1
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 F-manifolds, F-CohFTs, and integrable hierarchies
Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni +1
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 (homogen…
Open topological recursion relations in genus and integrable systems
Oscar Brauer, Alexandr Buryak
The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in ge…
Towards a bihamiltonian structure for the double ramification hierarchy
Alexandr Buryak, Paolo Rossi, Sergey Shadrin
We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomol…
Open r-spin theory I: Foundations
Alexandr Buryak, Emily Clader, Ran J. Tessler
We lay the foundation for a version of -spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of -spin disks, their moduli space,…
Open descendent theory I: The stationary sector
Alexandr Buryak, Amitai Netser Zernik, Rahul Pandharipande +1
We define stationary descendent integrals on the moduli space of stable maps from disks to . We prove a localization formula for the stationary theor…
Semisimple flat F-manifolds in higher genus
Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni +1
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…
Open Saito theory for and singularities
Alexey Basalaev, Alexandr Buryak
A well known construction of B. Dubrovin and K. Saito endows the parameter space of a universal unfolding of a simple singularity with a Frobenius manifold structure. In our paper…
Quadratic double ramification integrals and the noncommutative KdV hierarchy
Alexandr Buryak, Paolo Rossi
In this paper we compute the intersection number of two double ramification cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli…
Open WDVV equations and Virasoro constraints
Alexey Basalaev, Alexandr Buryak
In their fundamental work, B. Dubrovin and Y. Zhang, generalizing the Virasoro equations for the genus 0 Gromov-Witten invariants, proved the Virasoro equations for a descendent po…
Open -spin theory II: The analogue of Witten's conjecture for -spin disks
Alexandr Buryak, Emily Clader, Ran J. Tessler
We conclude the construction of -spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open -spin intersection numbers, and we prove that the…
Simple Lax Description of the ILW Hierarchy
Alexandr Buryak, Paolo Rossi
In this note we present a simple Lax description of the hierarchy of the intermediate long wave equation (ILW hierarchy). Although the linear inverse scattering problem for the ILW…