Pavel Nikolaevich Pyatov
- Deputy Dean for Admissions, Professor:Faculty of Mathematics
- Pavel Nikolaevich Pyatov has been at HSE University since 2009.
Education and Degrees
- 2020
Doctor of Sciences*
HSE University - 1991
Candidate of Sciences* (PhD) in Mathematical Physics
Institute of High-Energy Physics
Thesis Title: Lagrangian formalism for constrained systems - 1987
Degree in Physics
Lomonosov Moscow State University, Department of Physics
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.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Courses (2022/2023)
Differential Equations (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 2 year, 1, 2 module)Rus
- Research Seminar "Braid Group, Quantum Groups and Applications" (Optional course (faculty); 3, 4 module)Rus
- Research Seminar "Mathematical Foundations of Quantum Mechanics" (Optional course (faculty); 1, 2 module)Rus
Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 3 year, 3, 4 module)Rus
- Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
- Past Courses
Courses (2021/2022)
- Braid Group, Quantum Groups and Applications (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Research Seminar "Mathematical Foundations of Quantum Mechanics" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; 3 year, 3, 4 module)Rus
- Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
Courses (2020/2021)
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematical Foundations of Quantum Mechanics (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Mechanics (Bachelor’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
- Research Seminar "Braid Groups, Quantum Groups and Applications" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2019/2020)
- Research Seminar "Braid Group, R-matrices, and Quantum Groups" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Rus
Courses (2018/2019)
- Classical Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Rus
- Research Seminar "Selcted Topics from Braid Group Theory and Qauntum Groups: Genesis and Applications of R-Matrices" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2017/2018)
- Classical Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Physics; 1 year, 3, 4 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematical Practical Training 2 (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 1 year, 1-4 module)Rus
- Mechanics (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Rus
- Research Seminar "The R-matrix: its Origin and Applications in the Braid Group Theory and in Quantum Groups" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Conferences
- 2016
Classical and quantum integrable systems and supersymmetry (Тянцзинь). Presentation: de Rahm complex over quantum linear groups and dynamical R-martrices
- 2015Международной конференции «Классические и квантовые интегрируемые системы» (Протвино). Presentation: «Классические и квантовые интегрируемые системы»
Publications40
- Article Ogievetsky O., Pyatov P. N. Cayley–Hamilton theorem for symplectic quantum matrix algebras // Journal of Geometry and Physics. 2021. Vol. 165. Article 104211. doi
- Article Ogievetsky O., Pyatov P. N. Quantum Matrix Algebras of BMW type: Structure of the Characteristic Subalgebra // Journal of Geometry and Physics. 2021. Vol. 162. Article 104086. doi
- Article Pyatov P. N., Trofimova A. Representations of finite-dimensional quotient algebras of the 3-string braid group // Moscow Mathematical Journal. 2021. Vol. 21. No. 2. P. 427-442. doi
- Preprint Pyatov P. N., Ogievetsky O. Cayley-Hamilton Theorem for Symplectic Quantum Matrix Algebras / Cornell University. Series math "arxiv.org". 2020.
- Preprint Ogievetsky O., Pyatov P. N. Quantum Matrix Algebras of BMW type: Structure of the Characteristic Subalgebra / Cornell University. Series math "arxiv.org". 2019. No. arXiv:1910.08551 .
- Article Pavel Pyatov, Povolotsky A. M., Rittenberg V. Large deviations of avalanches in the raise and peel model // Journal of Statistical Mechanics: Theory and Experiment. 2018. Vol. 2018. No. 053107. P. 1-26. doi
- Preprint Pavel Pyatov, Anastasia Trofimova. Representations of finite-dimensional quotient algebras of the 3-string braid group / Cornell University Library. Series math.RT "arXiv:1808.06395 [math.RT]". 2018.
- Article Pyatov P. N. On the construction of unitary quantum group differential calculus // Journal of Physics A: Mathematical and Theoretical. 2016. Vol. 49. No. 41. P. 415202-(25pp). doi
- Preprint Pyatov P. N. On construction of unitary quantum group differential calculus / Cornell University. Series "Working papers by Cornell University". 2015. No. 1504.04442 [math.QA].
- Article Francisco C. Alcaraz, Pavel Pyatov, Rittenberg V. Stochastic processes with $Z_N$ symmetry and complex Virasoro representations. The partition functions. // Journal of Physics A: Mathematical and Theoretical. 2014. Vol. 47. No. 46. P. 462001. doi
- Article Pyatov P. N., Gurevich D., Saponov P. A. Braided Weyl algebras and differential calculus on U(u(2)) // Journal of Geometry and Physics. 2012. Vol. 62. No. 5. P. 1175-1188. doi
- Article Gurevich D., Saponov P. A., Pyatov P. N. Braided differential operators on quantum algebra // Journal of Geometry and Physics. 2011. Vol. 61. P. 1485-1501.
- Article Gurevich D., Pyatov P. N., Saponov P. A. Bilinear identities on Schur symmetric functions // Journal of Nonlinear Mathematical Physics. 2010. Vol. 17. No. supp01. P. 31-48. doi
- Article Pyatov P. N., de Gier J. Factorized solutions of Temperley-Lieb qKZ equations on a segment // Advances in Theoretical and Mathematical Physics. 2010. Vol. 14. No. 3. P. 795-877.
- Article Pyatov P. N., de Gier J., Zinn-Justin P. Punctured plane partitions and the q-deformed Knizhnik--Zamolodchikov and Hirota equations // Journal of Combinatorial Theory, Series A. 2009. Vol. 116. P. 772-794.
- Article Gurevich D., Pyatov P. N., Saponov P. A. Representation theory of (modified) Reflection Equation Algebra of GL(m|n) type // St Petersburg Mathematical Journal. 2009. Vol. 20. P. 213-253.
- Article Isaev A. P., Pyatov P. N. Spectral extension of the quantum group cotangent bundle // Communications in Mathematical Physics. 2009. Vol. 288. P. 1137-1179. doi
- Article Gurevich D., Pyatov P. N., Saponov P. A. Spectral parameterization for power sums of a quantum supermatrix // Theoretical and Mathematical Physics. 2009. Vol. 159. P. 587-597.
- Article Alcaraz F. C., Pyatov P. N., Rittenberg V. Two-component abelian sandpile models // Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2009. Vol. 79. P. 1-4.
- Article Alcaraz F. C., Pyatov P. N., Rittenberg V. Density profiles in the raise and peel model with and without a wall. Physics and combinatorics // Journal of Statistical Mechanics: Theory and Experiment. 2008. Vol. P01006. P. 1-38.
- Article Gurevich D., Pyatov P. N., Saponov P. A. Reflection equation algebra in braided geometry // Journal of Generalized Lie Theory and Applications. 2008. Vol. 2. No. 3. P. 162-174.
- Article Пятов П. Н., Гуревич Д. И., Сапонов П. А. Теория представлений алгебры (модифицированного) уравнения отражений GL(m|n) типа // Алгебра и анализ. 2008. Т. 20. № 2. С. 70-133.
- Article Гуревич Д. И., Пятов П. Н., Сапонов П. А. Квантовые матричные алгебры GL(m|n) типа: структура характеристической подалгебры и ее спектральная параметризация // Теоретическая и математическая физика. 2006. Т. 147. № 1. С. 14-46.
- Article de Gier J., Nichols А., Pyatov P. N., Rittenberg V. Magic in the spectra of the XXZ quantum chain with boundaries at Δ=0 and Δ=-1/2 // Nuclear Physics B. 2005. Vol. 729. No. 3. P. 387-418.
- Article Гуревич Д. И., Пятов П. Н., Сапонов П. А. Теорема Кэли-Гамильтона для квантовых матричных алгебр GL(m|n) типа // Алгебра и анализ. 2005. Т. 17. № 1. С. 160-182.
- Article Pyatov P. N., de Gier J. Bethe ansatz for the Temperley-Lieb loop model with open boundaries // Journal of Statistical Mechanics: Theory and Experiment. 2004. No. P03002
- Article Pyatov P. N. Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon // Journal of Statistical Mechanics: Theory and Experiment. 2004. No. P09003. P. 1-30.
- Article Twarock R., Pyatov P. N. Construction of diffusion algebras // Journal of Mathematical Physics. 2002. Vol. 43. P. 3268.
- Article Isaev A. P., Pyatov P. N., Rittenberg V. Diffusion algebras // Journal of Physics A: Mathematical and Theoretical. 2001. Vol. 34
- Article Ogievetsky O., Pyatov P. N. Dynamical Cremmer-Gervais R-matrix // Physics of Atomic Nuclei. 2001. Vol. 64
- Article Isaev A. P., Hajiivanov L., Todorov I., Ogievetsky O., Pyatov P. N. Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras // Mathematical Physics Analysis and Geometry. 1999. Vol. 40. P. 427-448.
- Article Pyatov P. N., Isaev A. P., Ogievetsky O. On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities // Journal of Physics A: Mathematical and Theoretical. 1999. Vol. 32. P. 115-121.
- Article Isaev A. P., Ogievetsky O., Pyatov P. N. Generalized Cayley-Hamilton-Newton identities // Czechoslovak Journal of Physics. 1998. Vol. 48. No. 11. P. 1369-1374.
- Article Pyatov P. N., Gurevich D., Saponov P. A. Hecke symmetries and characteristic relations on reflection equation algebra // Letters in Mathematical Physics. 1997. Vol. 41. P. 255-264.
- Article Pyatov P. N., Faddeev L. The differential calculus on quantum linear groups // Transactions of the American Mathematical Society. 1996. Vol. 175. No. 2. P. 35-47.
- Article Pyatov P. N., Saponov P. A. Characteristic relations for quantum matrices // Journal of Physics A: Mathematical and Theoretical. 1995. Vol. 28. P. 4415-4421.
- Article Isaev A. P., Pyatov P. N. Covariant differential complexes on quantum linear groups // Journal of Physics A: Mathematical and Theoretical. 1995. Vol. 28. P. 2227-2246.
- Article Isaev A. P., Pyatov P. N. GLq(N)-covariant quantum algebras and covariant differential calculus // Physics Letters A. 1993. Vol. 179. P. 81-90.
- Article Razumov A., Pyatov P. N., Nirov K. Gauge invariance and constraints: open gauge algebras // International Journal of Modern Physics A. 1992. Vol. A7. P. 5549-5561.
- Article Разумов А., Пятов П. Н. Gauge invariance and constraints // International Journal of Modern Physics A. 1989. Т. A4