Petr E. Pushkar
- Associate Professor:Faculty of Mathematics
- Petr E. Pushkar has been at HSE University since 2010.
Education and Degrees
- 1999
Candidate of Sciences* (PhD)
Lomonosov Moscow State University - 1994
Degree
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.
Courses (2022/2023)
Calculus (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
Introduction to Differential Geometry (Master’s programme; Faculty of Mathematics; field of study "01.04.01. Математика", field of study "01.04.01. Математика", field of study "01.04.01. Математика", field of study "01.04.01. Математика", field of study "01.04.01. Математика"; 1 year, 1, 2 module)Eng
- Introduction to Differential Geometry (Optional course (faculty); 1, 2 module)Eng
- Research Seminar "An Introduction to Floer Homology" (Optional course (faculty); 3, 4 module)Eng
- Research Seminar "Smooth Manifolds" (Bachelor’s programme; Faculty of Mathematics; 4 year, 1-4 module)Rus
- Research Seminar "Smooth Manifolds" (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Theory of Complex Functions (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 2 year, 3, 4 module)Rus
- Past Courses
Courses (2021/2022)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Calculus (Bachelor’s programme; Faculty of Physics; 1 year, 1-4 module)Rus
- Introduction to Differential Geometry (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 2-4 module)Rus
- Research Seminar "Smooth Manifolds" (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
Theory of Complex Functions (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 2 year, 3, 4 module)Rus
Courses (2020/2021)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Introduction to Algebraic Topology (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 2, 3 module)Rus
- Research Seminar "Contact Topology and Invariants of Legendrian Knots" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Research Seminar "Morse Theory" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2019/2020)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Calculus (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Differential Geometric Structures (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- Introduction to Algebraic Topology (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Research Seminar "Mathematics Practical Training" (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Theory of Functions of Complex Variable (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
Courses (2018/2019)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematical Computations (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Eng
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Research Seminar "An Introduction to Symplectic and Contact geometry" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "Elements of Algebraic and Differential Topology" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
Courses (2017/2018)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Geometry (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Introduction to Topology (Smooth Manifolds) (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-3 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Research Seminar "Main Spectral Sequences 2" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
Courses (2016/2017)
Introduction to Discrete Mathematics (Bachelor’s programme; Faculty of Mathematics; 1 year, 4 module)Rus
Conferences
- 2014Ежегодная мемориальная конференция памяти Андрея Николаевича Тюрина (Москва). Presentation: Теория Морса на многообразиях с краем
- Ежегодная мемориальная конференция памяти Андрея Николаевича Тюрина (Москва). Presentation: Скрученные D-модули Уиттэкера и суперпотенциал Гайотто-Виттена
Publications17
- Article Petya Pushkar, Misha Temkin. Enhanced Bruhat Decomposition and Morse Theory // International Mathematics Research Notices. 2023. Vol. 00. P. 1-67. doi
- Article Тёмкин М. С., Пушкарь П. Е. О матрице дифференциала в комплексе Морса // Успехи математических наук. 2022. Т. 77. № 5. Статья 467. doi
- Article Пушкарь П. Е., Тёмкин М. С. Числа Брюа строгой функции Морса // Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2022. Т. 507. № 1. С. 57-60. doi
- Preprint Пушкарь П. Е., Тёмкин М. С. О матрице дифференциала в комплексе Морса / Математический институт им. В.А. Стеклова Российской академии наук. Серия 0000 "Сообщения Московского математического общества". 2021. (in press)
- Preprint Petr Pushkar, Misha Tyomkin. Enhanced Bruhat decomposition and Morse theory / https://arxiv.org/. Series 2012.05307 "arxiv.org". 2020.
- Preprint Pushkar P. E. Morse theory on manifolds with boundary I. Strong Morse function, cellular structures and algebraic simplification of cellular differential / Cornell University. Series arXiv "math". 2019. No. arXiv:1912.06437.
- Article Colin V., Ferrand E., Pushkar P. E. Positive Isotopies of Legendrian Submanifolds and Applications // International Mathematics Research Notices. 2017. Vol. 2017. No. 20. P. 6231-6254. doi
- Preprint Pushkar P. E. Chekanov-type theorem for spherized cotangent bundles / Cornell University. Series arXiv "math". 2016. No. arXiv:1602.08743.
- Preprint Pushkar P. E. On Hamiltonian and contact isotopy liftings / Cornell University. Series arXiv "math". 2016. No. arXiv:1602.07948.
- Preprint Pushkar P. E., Ferrand E., Colin V. Positive isotopies of Legendrian submanifolds and applications / Cornell University. Series math "arxiv.org". 2010. No. 1004.5263v1.
- Article Pushkar P. E., Ferrand E. Morse Theory and Global Coexistence of Singularities on Wave Fronts // Journal of London Mathematical Society. 2006. Vol. 74. No. 2. P. 527-544.
- Article Pushkar P. E., Чеканов Ю. В. Combinatorics of fronts of Legendrian links and the Arnol'd 4-conjectures // Russian Mathematical Surveys. 2005. Vol. 60. No. 1. P. 95-149.
- Article Pushkar P. E. On Functions Whose All Critical Points Are Contained in a Ball // Functional Analysis and Its Applications. 2002. Vol. 36. No. 4. P. 321-323.
- Article Pushkar P. E., Rudyak Y. On the minimal number of critical points of functions on h-cobordisms. // Mathematical Research Letters. 2002. Vol. 9. No. 9. P. 241-246.
- Article Pushkar P. E. Lagrange Intersections in a Symplectic Space // Functional Analysis and Its Applications. 2000. Vol. 34. No. 4. P. 288-292.
- Article Pushkar P. E. Generalizaton of the Chekanov Theorem. Diameters of Immersed Manifolds and Wave Fronts. // Proceedings of the Steklov Institute of Mathematics. 1998. Vol. 221. P. 279-295.
- Article Пушкарь П. Е. Производящие функции симплектоморфизмов // Функциональный анализ и его приложения. 1994. Т. 28. № 3. С. 61-65.