Publications

Preprints

1. A. Buryak, P. Rossi. Deformations of the Riemann hierarchy and the geometry of $\overline{M}_{g,n}$. arXiv:2504.02079.

Accepted for publication papers

1. A. Buryak, P. Rossi. Intersection numbers with Pixton's class and the noncommutative KdV hierarchy. Accepted for publication in the Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. arXiv:2308.13258.

Published papers

      2025

1. A. Buryak, P. Rossi. Bihamiltonian structure of the DR hierarchy in the semisimple case. Communications in Mathematical Physics 406 (2025), article number 205. Journal reference. arXiv:2408.12397.

2024

2. A. Yu. Buryak. DR-hierarchies: from the moduli spaces of curves to integrable systems. Proceedings of the Steklov Institute of Mathematics 325 (2024), 21-59. Journal reference.

3. A. Buryak, P. Rossi, D. Zvonkine. Moduli spaces of residueless meromorphic differentials and the KP hierarchy. Geometry and Topology 28 (2024), 2793-2824. Journal reference. arXiv:2110.01419.

4. A. Buryak, M. Troshkin. An application on the nonlinear reciprocal transformations in the theory of DR hierarchies. Moscow Mathematical Journal 24 (2024), no. 4, 513-527. Journal reference. arXiv:2310.10150.

5. X. Blot, A. Buryak. Quantum intersection numbers and the Gromov-Witten invariants of $CP^1$. Letters in Mathematical Physics 114 (2024), article number 131. Journal reference. arXiv:2402.16464.

6. A. Buryak, P. Rossi. Counting meromorphic differentials on $CP^1$. Letters in Mathematical Physics 114 (2024), article number 97. Journal reference. arXiv:2304.09557.

7. A. Buryak, S. Shadrin. Tautological relations and integrable systems. Epijournal de Geometrie Algebrique 8 (2024), https://doi.org/10.46298/epiga.2024.10382. Journal reference. arXiv:2210.07552.

8. A. Buryak, E. Clader, R. J. Tessler. Open r-spin theory II: The analogue of Witten's conjecture for r-spin disks. Journal of Differential Geometry 128 (2024), no. 1, 1-75. Journal reference. arXiv:1809.02536v4.

2023

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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

15. 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.

16. 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.

17. 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.

18. 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

19. 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.

20. 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.

21. 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.

22. 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.

23. 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.

24. 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.

25. 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

26. 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. 

27. 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

28. 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.

29. 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.

30. 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

31. 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.

32. 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

33. 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.

34. 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.

35. 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.

36. 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

37. 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.

38. 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.

39. A. Buryak. ILW equation for the Hodge integrals revisited. Mathematical Research Letters 23 (2016), no. 3, 675-683. Journal reference. arXiv:1505.05911.

40. 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.

41. 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.

42. 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

43. 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.

44. 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.

45. A. Buryak. Double ramification cycles and integrable hierarchies. Communications in Mathematical Physics 336 (2015), no. 3, 1085-1107. Journal reference. arXiv:1403.1719. 

46. 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.

47. 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.

48. 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

49. 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.

50. 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

51. 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. 

52. 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.

53. 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.

54. 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

55. 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.

56. A. Buryak. Bott's residue formula for singular varieties. TWMS Journal of Pure and Applied Mathematics 2 (2011), no.1, 17-21. Journal reference.

57. 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

58. 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.

59. 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.

60. 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 

• Amsterdam 

• Moscow (in Russian)