Pavel Nikolaevich Pyatov
- Deputy Head of the Laboratory:International Laboratory of Representation Theory and Mathematical Physics
- Associate Professor:Faculty of Mathematics / Joint Department with The Lebedev Physical Institute of the Russian Academy of Sciences
- Pavel Nikolaevich Pyatov has been at HSE University since 2009.
Education and Degrees
- 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
* 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.
Student Term / Thesis Papers
- Bachelor
A. Sheinkman «Gauss Decomposition for Reflection Equation Algebras». Faculty of Mathematics, 2019
A. Sotskiy «Combinatorial Properties of the Stationary States of Raise and Peel Models». Faculty of Mathematics, 2019
P. Filippova «Jucys-Murphy Elements in the Representation Theory of the Braid Group». Faculty of Mathematics, 2016
- Master
K. Boltaev «q-determinant in the Theory of Quantum Matrix Algebras: its Construction and Properties». Faculty of Mathematics, 2016
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
- Past Courses
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
- Mathematics Practical Training (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 of Master’s Programme (Master’s programme; Faculty of Mathematics; 2 year, 1-4 module)Eng
- 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
Courses (2016/2017)
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mechanics (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Rus
- Research Seminar of Master’s Programme (Master’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Research Seminar of Master’s Programme (Master’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Courses (2015/2016)
- Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mechanics and Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- String Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
Courses (2014/2015)
- Additional Chapters of Quantum Mechanics (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Advanced Topics in Mechanics and Field Theory (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematical Methods of Science (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mechanics and Field Theory (Bachelor’s programme; Faculty of Mathematics; 4 year, 1, 2 module)Rus
- Mechanics and Field Theory (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
- Mechanics and Field Theory (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 4 year, 3, 4 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 3 year, 3, 4 module)Rus
- Quantum Mechanics (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Research Seminar “Modern Problems in Mathematical Physics” I (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Research Seminar “Modern Problems in Mathematical Physics” III (Master’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Research Seminar “Modern Problems in Mathematical Physics” IV (Master’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
Courses (2013/2014)
- Advanced Topics in Quantum Mechanics (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematical Methods of Science (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Mechanics and Field Theory (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Mechanics and Field Theory (Bachelor’s programme; Faculty of Mathematics; 4 year, 1, 2 module)Rus
- Mechanics and Field Theory (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
- Quantum Mechanics (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 3 year, 3, 4 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 4 year, 3, 4 module)Rus
- Research Seminar “Modern Problems in Mathematical Physics” I (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Research Seminar “Modern Problems in Mathematical Physics” III (Master’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Eng
- Research Seminar “Modern Problems in Mathematical Physics” IV (Master’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Eng
Courses (2012/2013)
- Dynamic Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Introduction to Discrete Mathemetics (Bachelor’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Mathematical Methods of Science (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Eng
- Mechanics and Field Theory (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 4 year, 1, 2 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
Research Seminar "Advanced Topics in Quantum Mechanics" (Master’s programme; Faculty of Mathematics; field of study "010100.68 Математика", field of study "010100.68 Математика"; 1 year, 3, 4 module)Rus
- Research Seminar "Advanced Topics in Quantum Mechanics" (Bachelor’s programme; Faculty of Mathematics; 4 year, 3, 4 module)Rus
- Research Seminar "Advanced Topics in Quantum Mechanics" (Bachelor’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Research Seminar "Advanced Topics in Quantum Mechanics" (Bachelor’s programme; Faculty of Mathematics; 3 year, 3, 4 module)Rus
- Research Seminar "Advanced Topics in Quantum Mechanics" (Bachelor’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
- Research Seminar "Advanced Topics in Quantum Mechanics" (Master’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
Courses (2011/2012)
- Advanced Topics in Mathematical Physics (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Advanced Topics in Mathematical Physics (Master’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Introduction to Discrete Mathemetics (Bachelor’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
- Mathematics of Science (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 4 year, 1-3 module)Rus
- Quantum Mechanics (Bachelor’s programme; Faculty of Mathematics; 3 year, 1-4 module)Rus
Courses (2010/2011)
- Algebra (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 2-4 module)Rus
- Introduction to Discrete Mathemetics (Bachelor’s programme; Faculty of Mathematics; 1 year, 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»
Publications35
- 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
