Alexei Penskoi
- Professor:Faculty of Mathematics
- Alexei Penskoi has been at HSE University since 2013.
Education and Degrees
- 2013
Doctor of Sciences* in Geometry and Topology
Steklov Mathematical Institute of the Russian Academy of Sciences
Thesis Title: Geometry and Topology of Spectral Problems - 2001
PhD in Physical and Mathematical Sciences
University of Montreal
Thesis Title: Nonlinear ordinary differential equations with superposition principles - 1998
Candidate of Sciences* (PhD) in Geometry and Topology
Lomonosov Moscow State University
Thesis Title: Geometry and Hamiltonian formalism of integrable lattices - 1995
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.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
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
- Research Seminar "Riemannian Geometry" (Optional course (faculty); 1, 2 module)Rus
- Past Courses
Courses (2021/2022)
- Complex Geometry (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
Courses (2020/2021)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Differential Geometry (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2019/2020)
- Complex Geometry (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 "Mathematics Practical Training" (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Courses (2018/2019)
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 2, 3 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Research Seminar "Complex Geometry" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2017/2018)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 3 module)Rus
- Introduction to Topology (Smooth Manifolds) (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-3 module)Rus
- Mathematical Practical Training 2 (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Courses (2016/2017)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 3 module)Rus
Publications10
- Article Karpukhin M., Nadirashvili N., Penskoi Alexei V., Polterovich I. An isoperimetric inequality for Laplace eigenvalues on the sphere // Journal of Differential Geometry. 2021. Vol. 118. No. 2. P. 313-333. doi
- Article Nadirashvili N. S., Penskoi A. Free boundary minimal surfaces and overdetermined boundary value problems // Journal d'Analyse Mathematique. 2020. Vol. 141. P. 323-329. doi
- Article Пенской А. В. Изопериметрические неравенства для высших собственных значений оператора Лапласа–Бельтрами на поверхностях // Труды Математического института им. В.А. Стеклова РАН. 2019. Т. 305. С. 291-308. doi
- Article Penskoi Alexei V., Nadirashvili N. S. An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane // Geometric and Functional Analysis. 2018. Vol. 28. No. 5. P. 1368-1393. doi
- Preprint Penskoi A., Nadirashvili N. S., Berdnikov A. S. Bounds on Multiplicities of Laplace-Beltrami Operator Eigenvalues on the Real Projective Plane / Cornell University. Series arXiv "math". 2016.
- Article Penskoi A. Generalized Lawson Tori and Klein Bottles // Journal of Geometric Analysis. 2015. Vol. 25. No. 4. P. 2645-2666. doi
- Book Пенской А. В., Гайфуллин А. А., Смирнов С. В. Задачи по линейной алгебре и геометрии. М. : Московский центр непрерывного математического образования, 2014.
- Article Penskoi A. Extremal spectral properties of Otsuki tori // Mathematische Nachrichten. 2013. Vol. 286. No. 4. P. 379-391.
- Article Пенской А. В. Метрики, экстремальные для собственных чисел оператора Лапласа–Бельтрами на поверхностях // Успехи математических наук. 2013. Т. 68. № 6 (414). С. 107-168.
- Article Penskoi A. Extremal spectral properties of Lawson tau-surfaces and the Lam´e equation // Moscow Mathematical Journal. 2012. Vol. 12. No. 1. P. 173-192.
‘HSE Offers the Opportunity to Study Mathematics Alongside Renowned Mathematicians as Part of a Vibrant Research Community’
HSE University’s Faculty of Mathematics is one of the strongest in Russia, consistently ranking high on global university rankings. Its degree programmes attract the best students, not only from Russia, but also from around the world, by offering them a well-rounded mathematical education and a wide range of learning opportunities. In an interview with HSE News Service, a Master’s student and an HSE alum talk about features of the HSE Master’s Programme in Mathematics.