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.
Student Term / Thesis Papers
- Master
M. Tyomkin, On Bifurcations in One Paramentrical Morse Theory. Faculty of Mathematics, 2017
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, 2-4 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
- Past Courses
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
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Research Seminar "An Introduction to Surgery Theory" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "Morse Theory" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- Research Seminar "Symplectic Geometry and Topology" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
Courses (2015/2016)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Differential Geometry 1 (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematical Computations (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Eng
- Mathematics. Licenciatus (Bachelor’s programme; Faculty of Mathematics; 3 year, 4 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Research Seminar of Master’s Programme (Master’s programme; Faculty of Mathematics; 2 year, 1-4 module)Eng
- Singularity Theory 1 (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Singularity Theory 2 (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Symplectic Geometry and Topology (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
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
Publications12
- 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 arxive "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 arxive "math". 2016. No. arXiv:1602.08743.
- Preprint Pushkar P. E. On Hamiltonian and contact isotopy liftings / Cornell University. Series arxive "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.
