Alexei Yu. Pirkovskii
- Associate Professor:Faculty of Mathematics
- Alexei Yu. Pirkovskii has been at HSE University since 2010.
Education, Degrees and Academic Titles
- 2007Associate Professor
- 2000
Candidate of Sciences* (PhD) in Real, Complex and Functional Analysis
Lomonosov Moscow State University
Thesis Title: The existence problem for injective modules over "classical" topological algebras, and injective homological dimensions - 1997
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.
Research interests
Locally convex (in particular Banach) algebras and modules. Homological algebra in categories of topological modules: homological dimensions, Hochschild (co)homology of topological algebras etc. Topological algebras in noncommutative geometry and in quantum group theory.
Courses (2023/2024)
- C*-Algebras and Compact Quantum Groups (Optional course (faculty); 3, 4 module)Eng
Introduction to Discrete Mathematics and Topology (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 1 year, 1-3 module)Rus
- Introduction to Homotopical Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 4 module)Rus
- Research Seminar "Functional Analysis and Noncommutative Geometry 1" (Optional course (faculty); 1, 2 module)Rus
- Research Seminar "Functional Analysis and Noncommutative Geometry 2" (Optional course (faculty); 3, 4 module)Rus
- Topological Vector Spaces (Optional course (faculty); 1, 2 module)Eng
- Past Courses
Courses (2022/2023)
- Functional Analysis 2 (Optional course (faculty); 3, 4 module)Eng
- Research Seminar "Functional Analysis and Noncommutative Geometry 1" (Optional course (faculty); 1, 2 module)Rus
- Research Seminar "Functional Analysis and Noncommutative Geometry 2" (Optional course (faculty); 3, 4 module)Rus
- Research Seminar "Harmonic Analysis and Unitary Representations" (Optional course (faculty); 1, 2 module)Eng
Courses (2020/2021)
- Functional Analysis 2 (Operator Theory) (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Introduction to Functional Analysis (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Research Seminar "C*-Algebras and Compact Quantum Groups" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "Functional Analysis and Noncommutative Geometry 1" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Research Seminar "Functional Analysis and Noncommutative Geometry 2" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
Editorial board membership
2019: Member of the Editorial Board, Функциональный анализ и его приложения (Functional Analysis and Its Applications).
2011: Member of the Editorial Board, European Journal of Mathematics.
Conferences
- 2021Additive categories between algebra and functional analysis. Presentation: Flat locally convex modules beyond the metrizable case
- 2018Paweł Domański Memorial Conference, July 1-8, 2018 (Będlewo). Presentation: Dense quasi-free topological subalgebras of the Toeplitz algebra
- Conference on Partial Differential Equations and Applications in Memory of Professor B. Yu. Sternin (Москва). Presentation: Dense quasi-free subalgebras of the Toeplitz algebra
- 2014Workshop on Operator Spaces, Locally Compact Quantum Groups and Amenability (Торонто). Presentation: Taylor's functional calculus and derived categories
- Joint Meeting of the German Mathematical Society and the Polish Mathematical Society (Познань). Presentation: Taylor's functional calculus and derived categories of Fréchet modules
- 2013Integrable systems and Quantum symmetries (ISQS-21) (Прага). Presentation: Quantum polydisk, quantum ball, and a q-analog of Poincaré's theorem
- Banach Algebras and Applications (Banach Algebras 2013) (Гётеборг). Presentation: Quantum polydisk, quantum ball, and a q-analog of Poincaré's theorem
Publications21
- Article A. Yu. Pirkovskii. Dense quasi-free subalgebras of the Toeplitz algebra // Proceedings of the American Mathematical Society. 2023. Vol. 151. No. 4. P. 1681-1696. doi
- Article Pirkovskii A. Y., Piszczek K. Topological amenability and Köthe co-echelon algebras // Banach Journal of Mathematical Analysis. 2022. Vol. 16. No. 1. Article 13. doi
- Preprint Pirkovskii A. Y. A note on relative homological epimorphisms of topological algebras / Cornell University. Series math "arxiv.org". 2021. No. 2104.13716.
- Article Aristov O., A.Yu. Pirkovskii. Open embeddings and pseudoflat epimorphisms // Journal of Mathematical Analysis and Applications. 2020. Vol. 485. No. 2. Article 123817. doi
- Article Pirkovskii A. Y. Holomorphic functions on the quantum polydisk and on the quantum ball // Journal of Noncommutative Geometry. 2019. Vol. 13. No. 3. P. 857-886. doi
- Article Pirkovskii A. Y. Holomorphically finitely generated algebras // Journal of Noncommutative Geometry. 2015. Vol. 9. No. 1. P. 215-264. doi
- Preprint Pirkovskii A. Y. Quantized algebras of holomorphic functions on the polydisk and on the ball / Cornell University. Series math "arxiv.org". 2015. No. 1508.05768.
- Article Pirkovskii A. Y. Homological dimensions of modules of holomorphic functions on submanifolds of Stein manifolds // Journal of Functional Analysis. 2014. Vol. 266. No. 12. P. 6663-6683. doi
- Chapter Pirkovskii A. Y. Noncommutative analogues of Stein spaces of finite embedding dimension, in: Algebraic Methods in Functional Analysis. The Victor Shulman Anniversary Volume. Operator Theory: Advances and Applications, vol. 233. Basel : Birkhauser/Springer, 2014. Ch. 10. P. 135-153.
- Article Pirkovskii A. Y. Quantum polydisk, quantum ball, and a q-analog of Poincaré's theorem // Journal of Physics: Conference Series. 2013. Vol. 474. No. 012026. P. 1-14.
- Article Pirkovskii A. Y. Homological dimensions of Köthe algebras // Quarterly Journal of Mathematics. 2011. Vol. 62. No. 2. P. 487-499. doi
- Preprint Pirkovskii A. Y. The Arens-Michael envelope of a smash product / Cornell University. Series math "arxiv.org". 2011. No. 1101.0166.
- Article Pirkovskii A. Y. Flat cyclic Fr'echet modules, amenable Fr'echet algebras, and approximate identities // Homology, Homotopy and Applications. 2009. Vol. 11. No. 1. P. 81-114.
- Article Pirkovskii A. Y. Approximate characterizations of projectivity and injectivity for Banach modules // Mathematical Proceedings of the Cambridge Philosophical Society. 2007. Vol. 143. No. 2. P. 375-385.
- Article Pirkovskii A. Y. Arens-Michael enveloping algebras and analytic smash products // Proceedings of the American Mathematical Society. 2006. Vol. 134. No. 9. P. 2621-2631.
- Article Pirkovskii A. Y. Stably flat completions of universal enveloping algebras // Dissertationes Mathematicae. 2006. No. 441. P. 1-60.
- Article Pirkovskii A. Y. Biprojectivity and biflatness for convolution algebras of nuclear operators // Canadian Mathematical Bulletin. 2004. Vol. 47. No. 3. P. 445-455.
- Article Pirkovskii A. Y. Biprojective topological algebras of homological bidimension 1 // Journal of Mathematical Sciences. 2002. Vol. 111. No. 2. P. 3476-3495.
- Article Pirkovskii A. Y. On Arens-Michael algebras which do not have nonzero injective $\mathop{\widehat{\otimes}}$-modules // Studia Mathematica. 1999. Vol. 133. No. 2. P. 163-174.
- Article Pirkovskii A. Y. On certain homological properties of Stein algebras // Journal of Mathematical Sciences. 1999. Vol. 95. No. 6. P. 2690-2702.
- Article Pirkovskii A. Y. On the nonexistence of cofree Fr\'echet modules over locally multiplicatively-convex Fr\'echet algebras // Rocky Mountain Journal of Mathematics. 1999. Vol. 29. No. 3. P. 1129-1138.
‘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.