Богомолов Федор Алексеевич
Лаборатория алгебраической геометрии и ее приложений
Профессиональные интересы
Должности
- научный руководитель — Лаборатория алгебраической геометрии и ее приложений
Био
- · Начал работать в НИУ ВШЭ в 2010 году.
- · Научно-педагогический стаж: 15 лет.
Образование
- 1983 · Доктор физико-математических наук
- 1970 · Специалитет: Московский государственный университет им. М.В. Ломоносова, специальность «Математика», квалификация «Математик»
Опыт работы
- · 2010 г.: с Научный руководитель, Лаборатория алгебраической геометрии и ее приложений
Награды и поощрения
- · Silver Professor New York University (2016)
- · Почетная грамота Высшей школы экономики (октябрь 2021)
- · Благодарственное письмо ректора НИУ ВШЭ (сентябрь 2021)
- · Медаль "За вклад в науку и просвещение" (октябрь 2017)
- · Благодарность Высшей школы экономики (ноябрь 2016)
Гранты и проекты
- — · Совет по грантам Правительства РФ продлил еще на два года финансирование двух международных лабораторий ВШЭ, возглавляемых ведущими зарубежными учеными — Лаборатории сравнительных социальных исследований и Лаборатории алгебраической геометрии и ее приложений.
Конференции (36)
Показать все
- · 2021: Семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: О некоторых вопросах комплексной и арифметической геометрии II
- · 2021: Summer Geometry Fest (Moscow). Доклад: Second Chern classes of vector bundles and related geometry
- · 2020: Семинар Лаборатории алгебраической геометрии (Москва). Доклад: Several remarks on results in group theory and represnetation theory of finite groups
- · 2019: Семинар лаборатории алгебраической геометрии (Москва). Доклад: On base varieties of lagrangian abelian fibrations on projective hyperkahler manifolds
- · 2019: "Birational Geometry and Fano varieties" dedicated to V. Iskovskikh (Москва). Доклад: Group theoretic prove of the classification ofVII0surfaces with b2= 0
- · 2019: Летняя математическая школа Алгебра и Теория Чисел (Вороново). Доклад: Некоторые вопросы теории эллиптических кривых
- · 2019: Семинар лаборатории алгебраической геометрии (Москва). Доклад: On some problems in algebraic geometry and related areas
- · 2019: Современная геометрия и ее приложения - 2019 (Казань). Доклад: Некоторые открытые проблемы в комплексной и алгебраической геометрии
- · 2018: Семинар лаборатории алгебраической геометрии (Москва). Доклад: Абелевы расслоения
- · 2018: Семинар лаборатории алгебраической геометрии (Москва). Доклад: On $j$ invariants of the projective images of $4$-tuples torsion points
- · 2018: Geometry at Large, Symmetries and Correspondences ("Геометрия в целом, симметрии и соответствия") (Фуэртевентура). Доклад: On geometry over small fields ("O геометрии над малыми полями")
- · 2018: Geometry at Large, Symmetries and Correspondences ("Геометрия в целом, симметрии и соответствия") (Фуэртевентура). Доклад: Projective invariants of collections of torsion points of elliptic curves (Проективные инварианты наборов точек кручения на эллиптических кривых)
- · 2017: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: Geometry of sets of torsion points on elliptic curves
- · 2017: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: Комплексные поверхности типа VII_0 и теория групп
- · 2017: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: $PGL(2)$-invariants of collections of torsion points of elliptic curves
- · 2016: 2-я МЕЖДУНАРОДНАЯ НАУЧНАЯ КОНФЕРЕНЦИЯ - НАУКА БУДУЩЕГО (Казань). Доклад: Algebraic geometry
- · 2016: Workshop on Algebraic Geometry (Ханга Роа). Доклад: LEMMA ON INTERSECTION OF CURVES AND DOMAINS IN COMPLEX PROJECTIVE VARIETIES AND APPLICATIONS
- · 2016: Еженедельный семинар Лаборатории алгебраической геометрии (Москва). Доклад: I am going to consider the subsets of points in a complex projective line obtained as the image of torsion points under standard projection which is a quotient by the involution. These sets have finite intersections for different curves. Moreover I am going to show that in many cases the corresponding sets are quite small. I am also going to discuss some applications to geometry of hyperbolic curves.
- · 2016: Еженедельный семинар Лаборатории алгебраической геометрии (Москва). Доклад: Affine structures and VII_0 surfaces
- · 2015: Hyperbolicity in algebraic geometry (Ilhabela). Доклад: Closed symmetric differentials on projective surfaces
- · 2015: Magadan Algebraic Geometry International Conference (Магадан (Magadan)). Доклад: TORSION POINTS ON ELLIPTIC CURVES
- · 2015: Magadan Algebraic Geometry International Conference (Магадан (Magadan)). Доклад: SOME OPEN PROBLEMS IN ARITHMETIC ALGEBRAIC GEOMETRY
- · 2015: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: Torsion points on elliptic curves and related questions in algebra and geometry
- · 2014: Исследовательский семинар Университета Ноттингема (Nottingham). Доклад: Tate conjecture and relations in Galois groups
- · 2014: International conference "Algebraic Geometry and Number Theory" on the occasion of M.A. Tsfasman's and S.G. Vladuts' 60th birthday (Москва (Moscow)). Доклад: Homomorphisms of multiplicative groups of fields and section conjecture
- · 2014: Frontiers of Rationality (Longyearbyen). Доклад: Homomorphisms of Multyplicative Groups of Fields and Section Conjecture
- · 2014: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: Closed symmetric differentials on surfaces
- · 2014: Symmetries and Correspondences: Higher Structures in Number Theory (Ноттингем (Nottingham)). Доклад: Projective geometry and non-archimedean valuations
- · 2014: Symmetries and correspondences in number theory, geometry, algebra, physics: intra-disciplinary trends (Ноттингем (Nottingham)). Доклад: On the section conjecture in anabelian geometry
- · 2014: Second ERC Research Period on Diophantine Geometry (Diophantine Geometry, Unlikely Intersections and Algebraic Dynamics) (Четраро (Cetraro)). Доклад: Braid group and Szpiroine quality
- · 2013: LMS Invited Lectures 2013: Fedor Bogomolov (Эдинбург). Доклад: Серия лекций "Birational Geometry and Galois Groups"
- · 2013: Международная конференция "Глобальные поля" (Москва). Доклад: Inducing nonramified cohomology elements
- · 2013: Workshop "Foliation Theory in Algebraic Geometry" (Нью-Йорк). Доклад: Closed symmetric differentials on surfaces
- · 2013: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: On Szpiro's conjecture, it's relation to ABC-conjecture and some other problems in arithmetic geometry
- · 2013: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: Homomorphisms between multiplicative groups of fields and Grothendieck Section Conjecture
- · 2012: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: Группы подстановок и проективные группы
Идентификаторы исследователя
- ORCID:
0000-0003-3464-6494 - ResearcherID:
J-2655-2015 - SPIN РИНЦ:
6211-4553 - Google Scholar: http://scholar.google.ru/citations?hl=ru&user=_kTMRyoAAAAJ&view_op=list_works&authuser=1
- Scopus AuthorID:
6603748855
Публикации (74)
Stabilization of direct images for curves
2025 · PREPRINT · en
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree.
Geometric properties of curves defined over number fields
2022 · ARTICLE · en
The article contains a detailed proof of the famous Belyi theorem on geometry of complex algebraic curves defined over number fields. It also includes the discussion of several constructions and conjectures inspired by Belyi’s result which where brought up by the first author during his colloquium talks at different universities within the period from 1979 to 1984.
Geometry and Automorphisms of Non-Kähler Holomorphic Symplectic Manifolds
2022 · ARTICLE · en
We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works by D. Guan and the 1st author. Any such manifold Q of dimension 2n−2 is obtained as a finite degree n2 cover of some non-Kähler manifold WF, which we call the base of Q. We show that the algebraic reduction of Q and its base is the projective space of dimension n−1. Besides, we give a partial classification of submanifolds in Q, describe the degeneracy locus of its algebraic reduction and prove that the automorphism group of Q satisfies the Jordan property.
Stable vector bundles on the families of curves
2022 · ARTICLE · en
We offer a new approach to proving the Chen–Donaldson–Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a family of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.
Sections of Lagrangian fibrations on holomorphically symplectic manifolds and degenerate twistorial deformations
2022 · ARTICLE · en
Let (M,I,Ω) be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration π:M↦X, and η a closed form of Hodge type (1,1)+(2,0) on X. We prove that Ω′:=Ω+π∗η is again a holomorphically symplectic form, for another complex structure I′, which is uniquely determined by Ω′. The corresponding deformation of complex structures is called "degenerate twistorial deformation". The map π is holomorphic with respect to this new complex structure, and X and the fibers of π retain the same complex structure as before. Let s be a smooth section of of π. We prove that there exists a degenerate twistorial deformation (M,I′,Ω′) such that s is a holomorphic section.
Algebraically hyperbolic manifolds have finite automorphism groups
2020 · ARTICLE · en
A projective manifold M is algebraically hyperbolic if there exists a positive constant A such that the degree of any curve of genus g on M is bounded from above by A(g−1). A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here, we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.
Stable vector bundles on the families of curves
2020 · PREPRINT · en
We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.
On the PGL_2-invariant quadruples of torsion points of elliptic curves
2020 · ARTICLE · en
Let E be an elliptic curve and 𝜋:𝐸→ℙ^1 a standard double cover identifying ±𝑃∈𝐸. It is known that for some torsion points 𝑃_𝑖 ∈ 𝐸, 1⩽𝑖⩽4, the cross ratio of {𝜋(𝑃𝑖)}^4_{𝑖=1} is independent of E. We will give a complete classification of such quadruples.
Homomorphisms of multiplicative groups of fields preserving algebraic dependence
2019 · ARTICLE · en
We study homomorphisms of multiplicative groups of fields preserving algebraic dependence and show that such homomorphisms give rise to valuations.
Purely noncommuting groups
2019 · ARTICLE · en
We define and investigate a class of groups characterized by a representation-theoretic property, called purely noncommuting or PNC. This property guarantees that the group has an action on a smooth projective variety with mild quotient singularities. It has intrinsic group-theoretic interest as well. The main results are as follows. (i) All supersolvable groups are PNC. (ii) No nonabelian finite simple groups are PNC. (iii) A metabelian group is guaranteed to be PNC if its commutator subgroup’s cyclic prime-power-order factors are all distinct, but not in general. We also give a criterion guaranteeing a group is PNC if its nonabelian subgroups are all large, in a suitable sense, and investigate the PNC property for permutations.
Курсы (0)
Нет курсов.