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
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)
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.