67 citations · 510 across the 48 of their papers we have counts for
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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 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…
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…
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…
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…
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…
Extended -spin theory in all genera and the discrete KdV hierarchy
Alexandr Buryak, Paolo Rossi
In this paper we construct a family of cohomology classes on the moduli space of stable curves generalizing Witten's -spin classes. They are parameterized by a phase space which…
Extended -spin theory and the mirror symmetry for the -singularity
Alexandr Buryak
By a famous result of K. Saito, the parameter space of the miniversal deformation of the -singularity carries a Frobenius manifold structure. The Landau-Ginzburg mirror sy…
Closed extended -spin theory and the Gelfand-Dickey wave function
Alexandr Buryak, Emily Clader, Ran J. Tessler
We study a generalization of genus-zero -spin theory in which exactly one insertion has a negative-one twist, which we refer to as the "closed extended" theory, and which is clo…
DR/DZ equivalence conjecture and tautological relations
Alexandr Buryak, Jérémy Guéré, Paolo Rossi
In this paper we present a family of conjectural relations in the tautological ring of the moduli spaces of stable curves which implies the strong double ramification/Dubrovin-Zhan…
Double ramification cycles and the -point function for the moduli space of curves
Alexandr Buryak
In this paper, using the formula for the integrals of the -classes over the double ramification cycles found by S. Shadrin, L. Spitz, D. Zvonkine and the author, we derive a new…
The hypergeometric functions of the Faber-Zagier and Pixton relations
A. Buryak, F. Janda, R. Pandharipande
The relations in the tautological ring of the moduli space M_g of nonsingular curves conjectured by Faber-Zagier in 2000 and extended to the moduli space of stable pointed curves b…
Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary
A. Buryak
In a recent paper R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. The authors conjec…
Top tautological group of
A. Buryak, S. Shadrin, D. Zvonkine
We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus curves with marked points.
A simple proof of the formula for the Betti numbers of the quasihomogeneous Hilbert schemes
A. Buryak, B. L. Feigin, H. Nakajima
In a recent paper the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple de…
Integrals of psi-classes over double ramification cycles
A. Buryak, S. Shadrin, L. Spitz +1
DR-cycles are certain cycles on the moduli space of curves. Intuitively, they parametrize curves that allow a map to \mathbb{P}^1 with some specified ramification profile over two…
Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes
A. Buryak, B. L. Feigin
In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infin…
Homogeneous components in the moduli space of sheaves and Virasoro characters
A. Buryak, B. L. Feigin
The moduli space of framed torsion free sheaves on the projective plane with rank and second Chern class equal to has the natural action of the -di…
The moduli space of sheaves and the generalization of MacMahon's formula
A. Buryak
Recently M. Vuletic found a two-parameter generalization of the MacMahon's formula. In this note we show that certain ingredients of her formula have a clear interpretation in term…
The classes of the quasihomogeneous Hilbert schemes of points on the plane
A. Buryak
In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of -quasi-homogeneous Hilbert sche…
A new proof of Faber's intersection number conjecture
A. Buryak, S. Shadrin
We give a new proof of Faber's intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves $\M_g$. The proof is based on…
Existence of a singular projective variety with an arbitrary set of characteristic numbers
A. Y. Buryak
It is known that Chern characteristic numbers of compact complex manifolds cannot have arbitrary values. They satisfy certain divisability conditions. W. Ebeling and S. M. Gusein-Z…