Publications
Preprints
X. Blot, A. Buryak. Quantum intersection numbers and the Gromov--Witten invariants of $CP^1$. arXiv:2402.16464.
A. Buryak, M. Troshkin. An application on the nonlinear reciprocal transformations in the theory of DR hierarchies. arXiv:2310.10150.
A. Buryak, P. Rossi. Intersection numbers with Pixton's class and the noncommutative KdV hierarchy. arXiv:2308.13258.
A. Buryak, P. Rossi. Counting meromorphic differentials on $CP^1$. arXiv:2304.09557.
A. Buryak, S. Shadrin. Tautological relations and integrable systems. arXiv:2210.07552.
Accepted for publication papers
A. Buryak, P. Rossi, D. Zvonkine. Moduli spaces of residueless meromorphic differentials and the KP hierarchy. Accepted for publication in Geometry and Topology. arXiv:2110.01419.
A. Buryak, E. Clader, R. J. Tessler. Open r-spin theory II: The analogue of Witten's conjecture for r-spin disks. Accepted for publication in the Journal of Differential Geometry. arXiv:1809.02536v4.
Published papers
2023
A. Buryak, D. Gubarevich. Integrable systems of finite type from F-cohomological field theories without unit. Mathematical Physics, Analysis and Geometry 26 (2023), Article number 23. Journal reference. arXiv:2303.13356.
A. Buryak. A formula for the Gromov-Witten potential of an elliptic curve. Moscow Mathematical Journal 23 (2023), no. 3, 309-317. Journal reference. arXiv:2205.12777.
A. Buryak, E. Clader, R. J. Tessler. Open r-spin theory III: a prediction for higher genus. Journal of Geometry and Physics 192 (2023), 104960. Journal reference. arXiv:2211.16302.
A. Arsie, A. Buryak, P. Lorenzoni, P. Rossi. Semisimple flat F-manifolds in higher genus. Communications in Mathematical Physics 397 (2023), 141-197. Journal reference. arXiv:2001.05599.
A. Alexandrov, A. Basalaev, A. Buryak. A construction of open descendant potentials in all genera. International Mathematics Research Notices 2023 (2023), no. 17, 14840-14889. Journal reference. arXiv:2202.07312.
A. Buryak, P. Rossi. A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy. Journal of the Institute of Mathematics of Jussieu 22 (2023), no. 6, 2987-3009. Journal reference. arXiv:2103.04630.
2022
A. Buryak, F. Hernandez Iglesias, S. Shadrin. A conjectural formula for $DR_g(a,-a)\lambda_g$. Epijournal de Geometrie Algebrique 6 (2022), https://doi.org/10.46298/epiga.2022.8595. Journal reference. arXiv:2109.15245.
A. Buryak, A. Netser Zernik, R. Pandharipande, R. J. Tessler. Open $CP^1$ descendent theory I: The stationary sector. Advances in Mathematics 401 (2022), Paper No. 108249. Journal reference. arXiv:2003.00550.
A. Buryak, E. Clader, R. J. Tessler. Open r-spin theory I: Foundations. International Mathematics Research Notices 2022 (2022), no. 14, 10458-10532. Journal reference. arXiv:2003.01082.
A. Arsie, A. Buryak, P. Lorenzoni, P. Rossi. Riemannian F-manifolds, bi-flat F-manifolds, and flat pencils of metrics. International Mathematics Research Notices 2022 (2022), no. 21, 16730-16778. Journal reference. arXiv:2104.09380.
2021
O. Brauer, A. Buryak. The bi-Hamiltonian structures of the DR and DZ hierarchies in the approximation up to genus one. Functional Analysis and Its Applications 55 (2021), 272-285. Journal reference. arXiv:2107.06076.
A. Arsie, A. Buryak, P. Lorenzoni, P. Rossi. Flat F-manifolds, F-CohFTs, and integrable hierarchies. Communications in Mathematical Physics 388 (2021), 291-328. Journal reference. arXiv:2012.05332.
A. Buryak, P. Rossi. Extended r-spin theory in all genera and the discrete KdV hierarchy. Advances in Mathematics 386 (2021), Paper No. 107794. Journal reference. arXiv:1806.09825.
A. Buryak, P. Rossi, S. Shadrin. Towards a bihamiltonian structure for the double ramification hierarchy. Letters in Mathematical Physics 111 (2021), article number 13. Journal reference. arXiv:2007.00846.
A. Buryak, P. Rossi. Quadratic double ramification integrals and the noncommutative KdV hierarchy. Bulletin of the London Mathematical Society 53 (2021), no. 3, 843-854. Journal reference. arXiv:1909.11617.
O. Brauer Gomez, A. Buryak. Open topological recursion relations in genus 1 and integrable systems. Journal of High Energy Physics 2021 (2021), 48. Journal reference. arXiv:2008.06922.
A. Basalaev, A. Buryak. Open Saito theory for A and D singularities. International Mathematics Research Notices 2021 (2021), no. 7, 5460-5491. Journal reference. arXiv:1909.00598.
2020
A. Buryak. Extended r-spin theory and the mirror symmetry for the $A_{r-1}$-singularity. Moscow Mathematical Journal~20 (2020), no. 3, 475-493. Journal reference. arXiv:1802.07075.
A. Buryak, B. Dubrovin, J. Guere, P. Rossi. Integrable systems of double ramification type. International Mathematics Research Notices 2020 (2020), no. 24, 10381-10446. Journal reference. arXiv:1609.04059.
2019
A. Buryak, J. Guere, P. Rossi. DR/DZ equivalence conjecture and tautological relations. Geometry & Topology 23 (2019), no. 7, 3537-3600. Journal reference. arXiv:1705.03287.
A. Basalaev, A. Buryak. Open WDVV equations and Virasoro constraints. Arnold Mathematical Journal 5 (2019), no. 2-3, 145-186. Journal reference. arXiv:1901.10393.
A. Buryak, E. Clader, R. J. Tessler. Closed extended r-spin theory and the Gelfand-Dickey wave function. Journal of Geometry and Physics 137 (2019), 132-153. Journal reference. arXiv:1710.04829.
2018
A. Buryak, P. Rossi. Simple Lax description of the ILW hierarchy. SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 14 (2018), 120, 7 pages. Journal reference. arXiv:1809.00271.
A. Buryak, B. Dubrovin, J. Guere, P. Rossi. Tau-structure for the double ramification hierarchies. Communications in Mathematical Physics 363 (2018), no. 1, 191-260.Journal reference. arXiv:1602.05423.
2017
A. Y. Buryak. New approaches to integrable hierarchies of topological type. (Russian) Uspekhi Matematicheskikh Nauk 72 (2017), no. 5(437), 63-112. Translated in Russian Mathematical Surveys 72 (2017), no. 5, 841-887. Journal references: Russian version, English version.
A. Buryak, R. J. Tessler. Matrix models and a proof of the open analog of Witten's conjecture. Communications in Mathematical Physics 353 (2017), no. 3, 1299-1328. Journal reference. arXiv:1501.07888.
A. Buryak. Double ramification cycles and the n-point function for the moduli space of curves. Moscow Mathematical Journal 17 (2017), no. 1, 1-13. Journal reference. arXiv:1605.03736.
A. Alexandrov, A. Buryak, R. J. Tessler. Refined open intersection numbers and the Kontsevich-Penner matrix model. Journal of High Energy Physics 2017 (2017), 123.Journal reference. arXiv:1702.02319.
2016
A. Buryak, S. Shadrin, D. Zvonkine. Top tautological group of $M_{g,n}$. Journal of the European Mathematical Society 18 (2016), no. 12, 2925-2951. Journal reference. arXiv:1312.2775.
A. Buryak, J. Guere. Towards a description of the double ramification hierarchy for Witten's r-spin class. Journal de Mathematiques Pures et Appliquees 106 (2016), no. 5, 837-865. Journal reference. arxiv:1507.05882.
A. Buryak. ILW equation for the Hodge integrals revisited. Mathematical Research Letters 23 (2016), no. 3, 675-683. Journal reference. arXiv:1505.05911.
A. Buryak. Open intersection numbers and the wave function of the KdV hierarchy. Moscow Mathematical Journal 16 (2016), no. 1, 27-44. Journal reference. arXiv:1409.7957.
A. Buryak, P. Rossi. Double ramification cycles and quantum integrable systems. Letters in Mathematical Physics 106 (2016), no. 3, 289-317. Journal reference. arXiv:1503.03687.
A. Buryak, P. Rossi. Recursion relations for double ramification hierarchies. Communications in Mathematical Physics 342 (2016), no. 2, 533-568. Journal reference. arXiv:1411.6797.
2015
A. Buryak, F. Janda, R. Pandharipande. The hypergeometric functions of the Faber-Zagier and Pixton relations. Pure and Applied Mathematics Quarterly 11 (2015), no. 4, 591-631. Journal reference. arXiv:1502.05150.
A. Buryak. Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary. Letters in Mathematical Physics 105 (2015), no. 10, 1427-1448. Journal reference. arXiv:1409.3888.
A. Buryak. Double ramification cycles and integrable hierarchies. Communications in Mathematical Physics 336 (2015), no. 3, 1085-1107. Journal reference. arXiv:1403.1719.
A. Buryak. Dubrovin-Zhang hierarchy for the Hodge integrals. Communications in Number Theory and Physics 9 (2015), no. 2, 239-271. Journal reference. arXiv:1308.5716.
A. Buryak, B. L. Feigin, H. Nakajima. A simple proof of the formula for the Betti numbers of the quasihomogeneous Hilbert schemes. International Mathematical Research Notices 2015 (2015), no. 13, 4708-4715. Journal reference. arxiv:1302.2789.
A. Buryak, S. Shadrin, L. Spitz, D. Zvonkine. Integrals of $\psi$-classes over double ramification cycles. American Journal of Mathematics 137 (2015), no. 3, 699-737. Journal reference. arXiv:1211.5273.
2013
A. Buryak, B. L. Feigin. Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes. Symmetries, Integrable Systems and Representations, 15-33, Springer Proceedings in Mathematics and Statistics 40 (2013). Journal reference. arXiv:1206.5640.
A. Buryak. The moduli space of sheaves and the generalization of MacMahon's formula. Functional Analysis and Its Applications 47 (2013), no. 2, 96-103. Journal reference. arXiv:1101.0433.
2012
A. Buryak, B. L. Feigin. Homogeneous components in the moduli space of sheaves and Virasoro characters. Journal of Geometry and Physics 62 (2012), no. 7, 1652-1664. Journal reference. arXiv:1111.6422.
A. Buryak, H. Posthuma, S. Shadrin. On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket. Journal of Geometry and Physics 62 (2012), no. 7, 1639-1651. Journal reference. arXiv:1104.2722.
A. Buryak, H. Posthuma, S. Shadrin. A polynomial bracket for the Dubrovin-Zhang hierarchies. Journal of Differential Geometry 92 (2012), no. 1, 153-185. Journal reference. arXiv:1009.5351.
A. Buryak. The classes of the quasihomogeneous Hilbert schemes of points on the plane. Moscow Mathematical Journal 12 (2012), no. 1, 1-17. Journal reference. arXiv:1011.4459.
2011
A. Buryak, S. Shadrin. A new proof of Faber's intersection number conjecture. Advances in Mathematics 228 (2011), 22-42. Journal reference. arXiv:0912.5115.
A. Buryak. Bott's residue formula for singular varieties. TWMS Journal of Pure and Applied Mathematics 2 (2011), no.1, 17-21. Journal reference.
A. Buryak. First non-zero terms for the Taylor expansion at 1 of the Conway potential function. Moscow University Mathematics Bulletin 66 (2011), no. 1, 41-43. Journal reference.
2010
A. Buryak, S. Shadrin. A remark on deformations of Hurwitz Frobenius manifolds. Letters in Mathematical Physics 93 (2010), no. 3, 243-252. Journal reference. arXiv:0912.5114.
A. Buryak. Existence of a singular projective variety with an arbitrary set of characteristic numbers. Mathematical Research Letters 17 (2010), no. 3, 395-400. Journal reference. arXiv:0906.2287.
A. Buryak. The Poincare series of divisorial filtration associated with a curve with one branch at infinity. Mathematical Notes 87 (2010), no. 1-2, 52-58. Journal reference.
Thesis