Попов Владимир Леонидович
Московский институт электроники и математики им. А.Н. Тихонова
Профессиональные интересы
Должности
- Профессор — Московский институт электроники и математики им. А.Н. Тихонова, Департамент прикладной математики
Био
- · Начал работать в НИУ ВШЭ в 2012 году.
- · Научно-педагогический стаж: 52 года.
Образование
- 2016 · Член-корреспондент РАН
- 1986 · Ученое звание: Профессор
- 1984 · Доктор физико-математических наук: специальность 01.01.06 «Математическая логика, алгебра и теория чисел», тема диссертации: Группы, образующие, сизигии и орбиты в теории инвариантов
- 1972 · Кандидат наук: специальность 01.01.06 «Математическая логика, алгебра и теория чисел», тема диссертации: Стабильность действия алгебраических групп и арифметика квазиоднородных многообразий
- 1971 · Аспирантура: Московский государственный университет им. М.В. Ломоносова, факультет: механико-математический, специальность «математик»
- 1969 · Специалитет: Московский государственный университет им. М.В. Ломоносова, специальность «Математика», квалификация «Математик»
Опыт работы
- · 1972 г.: Информация из трудовой книжки В. Л. Попова: С 3 января по настоящее время на преподавательской работе в МИЭМ последовательно в должности ассистента, старшего преподавателя, доцента, профессора, заведующего кафедрой Алгебры и математической логики
Награды и поощрения
- · Надбавка за публикацию в журнале из Списка А (и приравненном к нему научном издании) (2025–2026, 2024–2025, 2023–2024)
- · Надбавка за публикацию в международном рецензируемом научном издании (2022–2023, 2021–2022, 2020–2022, 2019–2020, 2017–2018)
- · Надбавка за статью в зарубежном рецензируемом журнале (2015–2017, 2013–2015)
- · Лучший преподаватель — 2016–2020, 2014
Гранты и проекты
- 2025 · Руководитель гранта РНФ 23-11-00033 в 2023--2025 гг.
Идентификаторы исследователя
- ORCID:
0000-0003-0990-2898 - ResearcherID:
C-3495-2014 - SPIN РИНЦ:
4821-2463 - Google Scholar: https://scholar.google.com/citations?view_op=list_works&hl=ru&user=Qcve-A0AAAAJ&gmla=AJsN-F7_dfa-BKu5tKautOGbJNGt6M7MiyL94iQR_ro8z4hZwcVmK80OXZUPZGyoPPkJnDfbImEOHjz4LGPwSEHE7Bbhl30WdbukaSjWi6D_PhRo5XwwJx6A0PNxpZdReUGZVJMxhLeyEm9lOLh5orUnx624b67bpQ
- Scopus AuthorID:
13605069500
Публикации (115)
Faithful actions of automorphism groups of free groups on algebraic varieties
2023 · ARTICLE · en
Considering a certain construction of algebraic varieties X endowed with an algebraic action of the group Aut(F_n), n of this action. It gives an in nite family F of Xs such that Aut(F_n) embeds into Aut(X). For n > 2, this implies nonlinearity, and for n > 1, the existence of F_2 in Aut(X) (hence nonamenability of the latter) for X in F. We find in F two in finite subfamilies N and R consisting of irreducible ane varieties such that every X in N is nonrational (and even not stably rational), while every X in R is rational and 3n-dimensional. As an application, we show that the minimal dimension of affine algebraic varieties Z, for which Aut(Z) contains the braid group B_n on n strands, does not exceed 3n. This upper bound significantly strengthens the one following from the paper by D. Krammer [Kr02], where the linearity of B_n was proved (this latter bound is quadratic in n). The same upper bound also holds for Aut(F_n). In particular, it shows that the minimal rank of the Cremona groups containing Aut(F_n), does not exceed 3n, and the same is true for B_n.
Discrete complex reflection groups
2023 · ARTICLE · en
Это несколько отредактированный текст пяти лекций о моей классификации дискретных групп, порожденных отражениями эрмитовых аффинных пространств, которые я прочитал в октябре 1980 г. в университете Утрехта.
Групповые многообразия и групповые структуры
2022 · ARTICLE · ru
Мы исследуем в какой мере групповое многообразие связной алгебраической группы или вещественной группы Ли определяет ее групповую структуру.
Rationality of adjoint orbits
2022 · PREPRINT · en
We prove that every orbit of the adjoint representation of any connected reductive algebraic group G is a rational algebraic variety. For complex simply connected semisimple G, this implies rationality of affine Hamiltonian G-varieties (which we classify).
Faithful actions of automorphism groups of free groups on algebraic varieties
2022 · PREPRINT · en
Considering a certain construction of algebraic varieties X endowed with an algebraic action of the group Aut(Fn), n 3, this implies nonlinearity, and for n > 2, the existence of F2 in Aut(X) (hence nonamenability of the latter) forX ∈ F . We find in F two infinite subfamilies N and R consisting of irreducible affine varieties such that every X ∈ N is nonrational (and even not stably rational), while every X ∈ R is rational and 3n-dimensional. As an application, we show that the minimal dimension of affine algebraic varieties Z, for which Aut(Z) contains the braid group Bn on n > 3 strands, does not exceed 3n.This upper bound strengthens the one following from the paper by D. Krammer [Kr02], where the linearity of Bn was proved (this latter bound is quadratic in n). The same upper bound also holds for Aut(Fn). In particular, it shows that the minimal rank of theCremona groups containing Aut(Fn), does not exceed 3n, and the same is true for Bn if n > 3.
Embeddings of automorphism groups of free groups into automorphism groups of affine algebraic varieties
2022 · PREPRINT · en
A new infinite series of rational affine algebraic varieties is constructed whose automorphism group contains the auto\-morphism group Aut(F_n) of the free group F_n of rank n. The automorphism groups of such varieties are nonlinear and contain the braid group B_n on n strands for n > 2, and are nonamenable for n > 1. As an application, it is proved that for n\geqslant 3, every Cremona group of rank > 3n-2 contains the groups Aut(F_n) and B_n. This bound is 1 better than the one published earlier by the author; with respect to B_n the order of its growth rate is one less than that of the bound following from the paper by D. Krammer. The basis of the construction are triplets (G, R, n), where G is a connected semisimple algebraic group and R is a closed subgroup of its maximal torus.
On algebraic group varieties
2021 · PREPRINT · en
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
Root systems in number fields
2021 · ARTICLE · en
We classify the types of root systems R in the rings of integers of number fields K such that the Weyl group W(R) lies in the group L(K) generated by Aut(K) and multiplications by the elements of K*. We also classify the Weyl groups of root systems of rank n which are isomorphic to a subgroup of L(K) for a number field K of degree n over Q.
Underlying varieties and group structures
2021 · PREPRINT · en
Starting with exploration of the possibility to present the underlying variety of an affine algebraic group in the form of a product of some algebraic varieties, we then explore the naturally arising problem as to what extent the group variety of an algebraic group determines its group structure.
Embeddings of groups Aut(F_n) into automorphism groups of algebraic varieties
2021 · PREPRINT · en
For each integer n>0, we construct a series of irreducible algebraic varieties X, for which the automorphism group Aut(X) contains as a subgroup the automorphism group Aut(F_n) of a free group F_n of rank n. For n > 1, such groups Aut(X) are nonamenable, and for n > 2, they are nonlinear and contain the braid group B_n. Some of these varieties X are affine, and among affine, some are rational and some are not, some are smooth and some are singular. The byproduct is that for n > 2, each Cremona group of rank > 3n-1 contains Aut(F_n) and the braid group B_n.
Курсы (2)
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Математическая логика и теория алгоритмов · 5 раза
2025/2026, 2024/2025, 2023/2024, 2022/2023, 2021/2022 · Специалитет · рус
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Методы алгебраической геометрии в криптографии · 5 раза
2025/2026, 2024/2025, 2023/2024, 2022/2023, 2021/2022 · Специалитет · рус