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.

Professional Interests

morse theory contact geometry Symplectic Geometry

Research interests

Symplectic/Contact Geometry/Topology, Morse theory.

Courses (2023/2024)

Calculus 2 (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
Introduction to Differential Geometry (Optional course (faculty); 1, 2 module)Eng
Introduction to Differential Geometry (Master’s programme; Faculty of Mathematics; field of study "01.04.01. Математика", field of study "01.04.01. Математика"; 1 year, 1, 2 module)Eng
Past Courses

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

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 (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

2014
Ежегодная 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.

Morse theory and Morse inequalities on manifold with boundary.

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