Alexandr Buryak
- Associate Professor:Faculty of Mathematics
- Laboratory Head:Faculty of Mathematics / HSE – Skoltech International Laboratory of Representation Theory and Mathematical Physics
- Alexandr Buryak has been at HSE University since 2020.
Education and Degrees
- 2013
Candidate of Sciences* (PhD) in Geometry and topology
Lomonosov Moscow State University
Thesis Title: Cohomology of quasihomogeneous components in the moduli space of sheaves - 2013
PhD in Mathematics
University of Amsterdam
Thesis Title: Topology of the moduli space of curves and integrable hierarchies - 2009
Degree in Mathematics
Lomonosov Moscow State University
* Candidate of Sciences
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
Awards and Accomplishments
Dubrovin medal winner (July 2020)
WHITEHEAD PRIZE in recognition of his outstanding contributions to the study of moduli of curves and integrable systems (June 2019)
Moscow Mathematical Society award (October 2014)
Courses (2023/2024)
Academic Mentor's Seminar "Topology, Combinatorics and Representation Theory" (Master’s programme; Faculty of Mathematics; field of study "01.04.01. Математика", field of study "01.04.01. Математика"; 2 year, 1-4 module)Eng
- Geometry (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Past Courses
Courses (2022/2023)
Academic Mentor's Seminar "Topology, Combinatorics and Representation Theory" (Master’s programme; Faculty of Mathematics; field of study "01.04.01. Математика", field of study "01.04.01. Математика"; 1 year, 1-4 module)Eng
- Geometry (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Introduction to Riemann Surfaces (Optional course (faculty); 3, 4 module)Eng
Courses (2021/2022)
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 2-4 module)Rus
- Research Seminar "Integrable Systems as Systems of PDEs with an Infinite Dimensional Algebra of Symmetries" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
Courses (2020/2021)
- Discrete Mathematics (Bachelor’s programme; Faculty of Mathematics; 1 year, 1 module)Rus
- Graphs and Topology (Minor; Faculty of Mathematics; 3, 4 module)Rus
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 2-4 module)Rus
20227
- Article Alexandrov A., Basalaev A., Buryak A. A Construction of Open Descendant Potentials in All Genera // International Mathematics Research Notices. 2022. Vol. 2022. Article rnac240. doi
- Article Buryak A., Hernandez Iglesias F., Shadrin S. A conjectural formula for DRg(a,−a)λg // Epijournal de Geometrie Algebrique. 2022. Vol. 6. Article 8595. doi
- Article Buryak A., Rossi P. A generalisation of Witten’s conjecture for the Pixton class and the noncommutative kdV hierarchy // Journal of the Institute of Mathematics of Jussieu. 2022 doi
- Article Buryak A., Netser Zernik A., Pandharipande R., Tessler R. J. Open CP^1 descendent theory I: The stationary sector // Advances in Mathematics. 2022. Vol. 401. Article 108249. doi
- Article Buryak A., Clader E., Tessler R. J. Open 𝑟-Spin Theory I: Foundations // International Mathematics Research Notices. 2022. Vol. 2022. No. 14. P. 10458-10532. doi
- Article Buryak A., Arsie A., Lorenzoni P., Rossi P. Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics // International Mathematics Research Notices. 2022. Vol. 2022. No. 21. P. 16730-16778. doi (in press)
- Article Arsie A., Buryak A., Lorenzoni P., Rossi P. Semisimple Flat F-Manifolds in Higher Genus // Communications in Mathematical Physics. 2022 doi
20217
- Article Buryak A., Rossi P. Extended r-spin theory in all genera and the discrete KdV hierarchy // Advances in Mathematics. 2021. Vol. 386. No. 6. Article 107794. doi
- Article Arsie A., Buryak A., Lorenzoni P., Rossi P. Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies // Communications in Mathematical Physics. 2021. Vol. 388. P. 291-328. doi
- Article Basalaev A., Buryak A. Open Saito theory for A and D singularities // International Mathematics Research Notices. 2021. Vol. 2021. No. 7. P. 5460-5491. doi
- Article Brauer Gomez O., Buryak A. Open topological recursion relations in genus 1 and integrable systems // Journal of High Energy Physics. 2021. Vol. 2021. P. 1-15. doi
- Article Buryak A., Rossi P. Quadratic double ramification integrals and the noncommutative KdV hierarchy // Bulletin of the London Mathematical Society. 2021. Vol. 53. No. 3. P. 843-854. doi
- Article Buryak A., Rossi P., Shadrin S. Towards a bihamiltonian structure for the double ramification hierarchy // Letters in Mathematical Physics. 2021. Vol. 111. Article 13. doi
- Article Брауэр О., Буряк А. Ю. Бигамильтонова структура в иерархиях DR и DZ в приближении до рода один // Функциональный анализ и его приложения. 2021. Т. 55. № 4. С. 22-39. doi
20202
- Article Buryak A. Extended $r$-spin theory and the mirror symmetry for the $A_{r-1}$-singularity // Moscow Mathematical Journal. 2020. Vol. 20. No. 3. P. 475-493. doi
- Article Buryak A., Dubrovin B., Guere J., Rossi P. Integrable systems of double ramification type // International Mathematics Research Notices. 2020. Vol. 2020. No. 24. P. 10381-10446. doi
20193
- Article Buryak A., Clader E., Tessler R. J. Closed extended r-spin theory and the Gelfand-Dickey wave function // Journal of Geometry and Physics. 2019. Vol. 137. P. 132-153. doi
- Article Guere J., Rossi P., Buryak A. DR/DZ equivalence conjecture and tautological relations // Geometry and Topology. 2019. Vol. 23. No. 7. P. 3537-3600. doi
- Article Basalaev A., Buryak A. Open WDVV equations and Virasoro constraints // Arnold Mathematical Journal. 2019. Vol. 5. No. 2-3. P. 145-186. doi
20182
- Article Buryak A., Rossi P. Simple Lax description of the ILW hierarchy // Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2018. Vol. 14. No. 120. P. 1-7. doi
- Article Buryak A., Dubrovin B., Guere J., Rossi P. Tau-structure for the double ramification hierarchies // Communications in Mathematical Physics. 2018. Vol. 363. No. 1. P. 191-260. doi
20174
- Article Buryak A. Double ramification cycles and the n-point function for the moduli space of curves // Moscow Mathematical Journal. 2017. Vol. 17. No. 1. P. 1-13. doi
- Article Buryak A., Tessler R. J. Matrix models and a proof of the open analog of Witten's conjecture // Communications in Mathematical Physics. 2017. Vol. 353. No. 3. P. 1299-1328. doi
- Article Alexandrov A., Buryak A., Tessler R. J. Refined open intersection numbers and the Kontsevich-Penner matrix model // Journal of High Energy Physics. 2017. Vol. 2017. No. 123. P. 123. doi
- Article Буряк А. Ю. Новые подходы к иерархиям топологического типа // Успехи математических наук. 2017. Т. 72. № 5(437). С. 63-112. doi
20166
- Article Buryak A., Rossi P. Double ramification cycles and quantum integrable systems // Letters in Mathematical Physics. 2016. Vol. 106. No. 3. P. 289-317. doi
- Article Buryak A. ILW equation for the Hodge integrals revisited // Mathematical Research Letters. 2016. Vol. 23. No. 3. P. 675-683. doi
- Article Buryak A. Open intersection numbers and the wave function of the KdV hierarchy // Moscow Mathematical Journal. 2016. Vol. 16. No. 1. P. 27-44. doi
- Article Buryak A., Rossi P. Recursion relations for double ramification hierarchies // Communications in Mathematical Physics. 2016. Vol. 342. No. 2. P. 533-568. doi
- Article Buryak A., Shadrin S., Zvonkine D. Top tautological group of $M_{g,n}$ // Journal of the European Mathematical Society. 2016. Vol. 18. No. 12. P. 2925-2951. doi
- Article Buryak A., Guere J. Towards a description of the double ramification hierarchy for Witten's r-spin class // Journal de Mathématiques Pures et Appliquées. 2016. Vol. 106. No. 5. P. 837-865. doi
20156
- Article Buryak A., Feigin B. L., Nakajima H. A simple proof of the formula for the Betti numbers of the quasihomogeneous Hilbert schemes // International Mathematical Research Notices. 2015. Vol. 2015. No. 13. P. 4708-4715. doi
- Article Buryak A. Double ramification cycles and integrable hierarchies // Communications in Mathematical Physics. 2015. Vol. 336. No. 3. P. 1085-1107. doi
- Article Buryak A. Dubrovin-Zhang hierarchy for the Hodge integrals // Communications in Number Theory and Physics. 2015. Vol. 9. No. 2. P. 239-271. doi
- Article Buryak A. Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary // Letters in Mathematical Physics. 2015. Vol. 105. No. 10. P. 1427-1448. doi
- Article Buryak A., Shadrin S., Spitz L., Zvonkine D. Integrals of $\psi$-classes over double ramification cycles // American Journal of Mathematics. 2015. Vol. 137. No. 3. P. 699-737. doi
- Article Buryak A., Janda F., Pandharipande R. The hypergeometric functions of the Faber-Zagier and Pixton relations // Pure and Applied Mathematics Quarterly. 2015. Vol. 11. No. 4. P. 591-631. doi
20132
- Chapter Buryak A., Feigin B. L. Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes, in: Symmetries, Integrable Systems and Representations Vol. 40: Symmetries, Integrable Systems and Representations. Springer, 2013. doi
- Article Буряк А. Ю. Пространство модулей пучков и обобщение формулы Мак-Магона // Функциональный анализ и его приложения. 2013. Т. 47. № 2. С. 18-26. doi
20124
- Article Buryak A., Posthuma H., Shadrin S. A polynomial bracket for the Dubrovin-Zhang hierarchies // Journal of Differential Geometry. 2012. Vol. 92. No. 1. P. 153-185. doi
- Article Feigin B. L., Buryak A. Homogeneous components in the moduli space of sheaves and Virasoro characters // Journal of Geometry and Physics. 2012. Vol. 62. No. 7. P. 1652-1664. doi
- Article Buryak A., Posthuma H., Shadrin S. On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket // Journal of Geometry and Physics. 2012. Vol. 62. No. 7. P. 1639-1651. doi
- Article Buryak A. The classes of the quasihomogeneous Hilbert schemes of points on the plane // Moscow Mathematical Journal. 2012. Vol. 12. No. 1. P. 1-17. doi
20113
- Article Buryak A., Shadrin S. A new proof of Faber's intersection number conjecture // Advances in Mathematics. 2011. Vol. 228. P. 22-42. doi
- Article Buryak A. Bott's residue formula for singular varieties // TWMS Journal of Pure and Applied Mathematics. 2011. Vol. 2. No. 1. P. 17-21.
- Article Буряк А. Ю. Первые ненулевые члены разложения Тейлора с центром в точке 1 потенциальной функции Конвея // Вестник Московского университета. Серия 1: Математика. Механика. 2011. № 1. С. 57-59. doi
20103
- Article Buryak A., Shadrin S. A remark on deformations of Hurwitz Frobenius manifolds // Letters in Mathematical Physics. 2010. Vol. 93. No. 3. P. 243-252. doi
- Article Buryak A. Existence of a singular projective variety with an arbitrary set of characteristic numbers // Mathematical Research Letters. 2010. Vol. 17. No. 3. P. 395-400. doi
- Article Буряк А. Ю. Ряд Пуанкаре дивизориальной фильтрации, связанной с кривой с одной ветвью на бесконечности // Математические заметки. 2010. Т. 87. № 1. С. 60-68. doi
Conferences
- 2021Dynamics in Siberia (Новосибирск). Presentation: A noncommutative analog of Witten's conjecture
- International Congress on Mathematical Physics (Женева). Presentation: From curve counting theories to integrable systems
- Конференция «Дни геометрии в Новосибирске — 2021» (Новосибирск). Presentation: Подсчёт мероморфных дифференциальных форм с нулевыми вычетами на сфере и иерархия КП
- Конференция международных математических центров мирового уровня (Сочи). Presentation: От теорий подсчета кривых к интегрируемым системам
- 2020Дни геометрии в Новосибирске - 2020 (Новосибирск). Presentation: Обобщение теории Гивенталя и открытые инварианты Громова-Виттена
- 2019
3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop (Поханг). Presentation: Generalization of the Givental theory for the open WDVV equations
- Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives (Ярославль). Presentation: Generalization of the Givental theory for the oriented WDVV equations