Александр Буряк

ведущий научный сотрудник / Сколковский институт науки и технологий
доцент / Национальный исследовательский университет “Высшая школа экономики” / факультет математики

Образование, учёные степени

2009 / Московский государственный университет / магистратура / специальность “Математика”
2013 / PhD / тема диссертации “Топология пространства модулей кривых и интегрируемые иерархии”
2013 / Кандидат физико-математических наук / Московский государственный университет / тема диссертации “Когомологии квазиоднородных компонент в пространстве модулей пучков”

Профессиональные интересы
Алгебраическая геометрия, математическая физика, топология, комбинаторика

Публикации в реферируемых изданиях:

  1. A. Arsie, A. Buryak, P. Lorenzoni, P. Rossi, “Semisimple flat F-manifolds in higher genus”, Commun. Math. Phys. 397, 141–197 (2023). doi.org/10.1007/s00220-022-04450-6
  2. A. Buryak, P. Rossi, "Counting meromorphic differentials on CP1" [ PDF: English, arXiv: 2304.09557]
  3. A. Buryak, D. Gubarevich, "Integrable systems of finite type from F-cohomological field theories without unit" [ PDF: English, arXiv: 2303.13356]
  4. A. Alexandrov, A. Basalaev, A. Buryak, "A construction of open descendant potentials in all genera", International Mathematics Research Notices, 2022;, rnac240, doi.org/10.1093/imrn/rnac240 [ PDF: English, arXiv: 2202.07312]
  5. A. Buryak, F. Hernandez Iglesias, S. Shadrin, “A conjectural formula for $DR_g(a,-a)\lambda_g$”, Epijournal de Geometrie Algebrique 6 (2022), doi.org/10.46298/epiga.2022.8595 [ PDF: English, arXiv: 2109.15245]
  6. A. Buryak, P. Rossi, “A generalization of Witten’s conjecture for the Pixton class and the noncommutative KdV hierarchy” ournal of the Institute of Mathematics of Jussieu, (2022) 1-23. doi:10.1017/S1474748022000354 [ PDF: English, arXiv: 2103.04630]
  7. A. Buryak, A. Netser Zernik, R. Pandharipande, R. Tessler, “Open $CP^1$ descendent theory I: The stationary sector”, Advances in Mathematics, 401 (2022), No.108249, https://doi.org/10.1016/j.aim.2022.108249
  8. A. Buryak, E. Clader, R. J. Tessler, “Open r-spin theory I: Foundations”, International Mathematics Research Notices, V.2022, 14, July 2022, 10458–10532, doi.org/10.1093/imrn/rnaa345
  9. A. Arsie, A. Buryak, P. Lorenzoni, P. Rossi, “Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics”, International Mathematics Research Notices, v.2022(21), 2022, 16730–16778, doi.org/10.1093/imrn/rnab203
  10. A. Basalaev, A. Buryak, “Open Saito theory for A and D singularities”, Int. Math. Res. Notices, Volume 2021, Issue 7, April 2021, pp.5460–5491, doi.org/10.1093/imrn/rnz381 [ PDF: English, arXiv: 1909.00598]
  11. A. Buryak, E. Clader, R.J. Tessler, "Open r-spin theory III: a prediction for higher genus" [ PDF: English, arXiv: 2211.16302]
  12. A. Buryak, S. Shadrin, "Tautological relations and integrable systems" [ PDF: English, arXiv: 2210.07552]
  13. A. Buryak, " A formula for the Gromov-Witten potential of an elliptic curve " [ PDF: English, arXiv: 2205.12777]
  14. A. Buryak, P. Rossi, D. Zvonkine, “Moduli spaces of residueless meromorphic differentials and the KP hierarchy” [ PDF: English, arXiv: 2110.01419]
  15. A. Buryak, P. Rossi, “Extended r-spin theory in all genera and the discrete KdV hierarchy”, Adv. Math. 2021. Vol.386. No.6. Article 107794, doi.org/10.1016/j.aim.2021.107794 ​[ PDF: English, arXiv: 1806.09825 ]
  16. A. Arsie, A. Buryak, P. Lorenzoni, P. Rossi, “Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies”, Commun. Math. Phys. 388, 291–328 (2021) doi.org/10.1007/s00220-021-04109-8
  17. O. Brauer, A. Buryak, “Open topological recursion relations in genus 1 and integrable systems”, J. High Energ. Phys. 2021, 48 (2021), doi.org/10.1007/JHEP01(2021)048 [ PDF: English, arXiv: 2008.06922]
  18. A. Buryak, P. Rossi, “Quadratic double ramification integrals and the noncommutative KdV hierarchy”, B. Lond. Math. Soc. V.53(3) 2021 pp.843-854, doi.org/10.1112/blms.12464 ​[ PDF: English, arXiv: 1909.11617 ]
  19. A. Buryak, P. Rossi, S. Shadrin, “Towards a bihamiltonian structure for the double ramification hierarchy”, Lett Math Phys 111, 13 (2021) doi.org/10.1007/s11005-020-01341-6
  20. О. Брауэр, А. Ю. Буряк, “Бигамильтонова структура в иерархиях DR и DZ в приближении до рода один”, Функц. анализ и его прил., 55:4 (2021), 22–39; Funct. Anal. Appl., 55:4 (2021), 272–285, doi.org/10.1134/S001626632104002X
  21. A. Buryak, “Extended r-spin theory and the mirror symmetry for the $A_{r-1}$-singularity // Moscow Mathematical Journal. 2020. v.20(3) 475-493, doi:10.17323/1609-4514-2020-20-3-475-493
  22. A. Buryak, B. Dubrovin, J. Guere, P. Rossi, “Integrable Systems of Double Ramification Type”, International Mathematics Research Notices, v.2020(24) Dec 2020, 10381–10446, doi.org/10.1093/imrn/rnz029
  23. A. Buryak, E. Clader, R.J. Tessler, “Closed extended r-spin theory and the Gelfand–Dickey wave function”, J. of Geometry and Physics, v.137 (2019) 132-153, doi.org/10.1016/j.geomphys.2018.11.007
  24. J. Guere, P. Rossi, A. Buryak, “DR/DZ equivalence conjecture and tautological relations”, Geometry and Topology. 2019 v.23(7) 3537-3600, doi:10.2140/gt.2019.23.3537
  25. A. Basalaev, A. Buryak, “Open WDVV Equations and Virasoro Constraints”, Arnold Math J. 5, 145–186 (2019), doi.org/10.1007/s40598-019-00115-w
  26. A. Buryak, P. Rossi, “Simple Lax description of the ILW hierarchy”, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2018, v.14(120) 1-7, doi.org/10.3842/SIGMA.2018.120
  27. A. Buryak, B. Dubrovin, J. Guere, P. Rossi, “Tau-Structure for the Double Ramification Hierarchies”, Commun. Math. Phys. 363, 191–260 (2018) doi.org/10.1007/s00220-018-3235-4
  28. A. Buryak, “Double ramification cycles and the n-point function for the moduli space of curves”, Moscow Mathematical Journal, 2017 v.17(1) 1-13, doi:10.17323/1609-4514-2017-17-1-1-13
  29. A. Buryak,R.J. Tessler, “Matrix Models and A Proof of the Open Analog of Witten’s Conjecture”, Commun. Math. Phys. 353, 1299–1328 (2017), doi.org/10.1007/s00220-017-2899-5
  30. A. Alexandrov, A. Buryak, R.J. Tessler, “Refined open intersection numbers and the Kontsevich-Penner matrix model”, J. High Energ. Phys. 2017, 123 (2017), doi.org/10.1007/JHEP03(2017)123
  31. А. Буряк, “Новые подходы к иерархиям топологического типа”, УМН, 72:5(437) (2017), 63–112; Russian Math. Surveys, 72:5 (2017), 841–887, doi.org/10.1070/RM9777
  32. A. Buryak, P. Rossi, “Double Ramification Cycles and Quantum Integrable Systems”, Lett Math Phys 106, 289–317 (2016), doi.org/10.1007/s11005-015-0814-6
  33. A. Buryak, “ILW equation for the Hodge integrals revisited”, Mathematical Research Letters, 2016, v.23(3) 675-683, dx.doi.org/10.4310/MRL.2016.v23.n3.a5
  34. A. Buryak, “Open intersection numbers and the wave function of the KdV hierarchy”, Moscow Mathematical Journal, 2016, v.16(1) 27-44 doi:10.17323/1609-4514-2016-16-1-27-44
  35. A. Buryak, P. Rossi, “Recursion Relations for Double Ramification Hierarchies”, Commun. Math. Phys. 342, 533–568 (2016), doi.org/10.1007/s00220-015-2535-1
  36. A. Buryak, S. Shadrin, D. Zvonkine, “Top tautological group of M_{g,n}”, J. Eur. Math. Soc. 18 (2016), no.12, 2925–2951, doi:10.4171/JEMS/657
  37. A. Buryak, J. Guéré, “Towards a description of the double ramification hierarchy for Witten’s r-spin class”, Journal de Mathématiques Pures et Appliquées, v.106(5) 2016, 837-865, doi.org/10.1016/j.matpur.2016.03.013
  38. A. Buryak, B. Feigin, H. Nakajima, “A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes”, Intern. Math. Research Notices, v.2015 (13) 2015, 4708–4715, doi.org/10.1093/imrn/rnu076
  39. A. Buryak, “Double Ramification Cycles and Integrable Hierarchies”, Commun. Math. Phys. 336, 1085–1107 (2015), doi.org/10.1007/s00220-014-2235-2
  40. A. Buryak, “Dubrovin-Zhang hierarchy for the Hodge integrals”, Communications in Number Theory and Physics, 2015 v.9(2) 239-271б doi.org/10.4310/CNTP.2015.v9.n2.a1
  41. A. Buryak, “Equivalence of the Open KdV and the Open Virasoro Equations for the Moduli Space of Riemann Surfaces with Boundary”, Lett Math Phys 105, 1427–1448 (2015), doi.org/10.1007/s11005-015-0789-3
  42. A. Buryak, S. Shadrin, L. Spitz, D. Zvonkine, “Integrals of ψ-classes over double ramification cycles”, American J. of Mathematics, 2015б 137(3), 699-737 doi:10.1353/ajm.2015.0022
  43. A. Buryak, F. Janda, R. Pandharipande, “The hypergeometric functions of the Faber-Zagier and Pixton relations”, Pure and Applied Mathematics Quarterly, 2015, v.11(4) 591-631, dx.doi.org/10.4310/PAMQ.2015.v11.n4.a3
  44. A. Buryak, B. Feigin, “Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes”, In: Iohara, K., Morier-Genoud, S., Rémy, B. (eds) Symmetries, Integrable Systems and Representations. Springer Proceedings in Mathematics & Statistics, vol 40. Springer, London, doi.org/10.1007/978-1-4471-4863-0_2
  45. А. Буряк, “Пространство модулей пучков и обобщение формулы Мак-Магона”, Функц. анализ и его прил., 47:2 (2013), 18–26; Funct. Anal. Appl., 47:2 (2013), 96–103 doi.org/10.4213/faa3108
  46. A. Buryak, H. Posthuma, S. Shadrin, “A polynomial bracket for the Dubrovin-Zhang hierarchies” J. Differential Geom. 92(1): 153-185 Sep 2012, doi:10.4310/jdg/1352211225
  47. A. Buryak, B.L. Feigin, “Homogeneous components in the moduli space of sheaves and Virasoro characters”, J. of Geometry and Physics, v.62(7) 2012, 1652-1664, doi.org/10.1016/j.geomphys.2012.02.011
  48. A. Buryak, H. Posthuma, S. Shadrin, “On deformations of quasi-Miura transformations and the Dubrovin–Zhang bracket”, J. of Geometry and Physics, v.62(7) 2012, 1639-1651, doi.org/10.1016/j.geomphys.2012.03.006
  49. A. Buryak, “The classes of the quasihomogeneous Hilbert schemes of points on the plane”, Moscow Math J 2012 v.12(1) 1-17, <doi.org/10.17323/1609-4514-2012-12-1-21-36
  50. A. Buryak, S. Shadrin, “A new proof of Faber’s intersection number conjecture”, Advances in Math., 2011 v.228, 22-42 doi.org/10.1016/j.aim.2011.05.009
  51. A. Buryak, “Bott’s residue formula for singular varieties”, TWMS J. of Pure and Applied Math., 2011 v.2(1) 17-21
  52. A. Buryak, “First non-zero terms for the Taylor expansion at 1 of the Conway potential function”, Moscow Univ. Math. Bull. 66, 41–43 (2011) doi.org/10.3103/S0027132211010086
  53. A. Buryak, S. Shadrin, “A remark on deformations of Hurwitz Frobenius manifolds”, Lett Math Phys 93, 243–252 (2010), doi.org/10.1007/s11005-010-0410-8
  54. A. Buryak, “Existence of a singular projective variety with an arbitrary set of characteristic numbers”, Math. Research Lett. 2010 v.17(3) 395-400, /dx.doi.org/10.4310/MRL.2010.v17.n3.a2
  55. А. Буряк, “Ряд Пуанкаре дивизориальной фильтрации, связанной с кривой с одной ветвью на бесконечности”, Математические заметки, 2010, т.87(1) 60–68, doi.org/10.4213/mzm6380, Mathematical Notes, 2010, v.87(1) 52–58 doi.org/10.1134/S0001434610010074