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)
A Constructive Proof of Brauer's Theorem on Induced Characters in the Group Ring
2014 · ARTICLE · en
We provide an alternative constructive proof of the classical Brauer theorem for finite groups based on the well-known description of the complex irreducible representations of the symmetric groups Sn . The theorem is first proved for Sn and then for general G by embedding in Sn and applying the Mackey subgroup theorem.
Local structure of closed symmetric 2-differentials
2014 · PREPRINT · en
In the authors's previous work on symmetric differentials and their connection to the topological properties of the ambient manifold, a class of symmetric differentials was introduced: closed symmetric differentials ([BoDeO11] and [BoDeO13]). In this article we give a description of the local structure of closed symmetric 2-differentials on complex surfaces, with an emphasis towards the local decompositions as products of 1-differentials. We show that a closed symmetric 2-differential $w$ of rank 2 (i.e. defines two distinct foliations at the general point) has a subvariety $B_w\subset X$ outside of which $w$ is locally the product of closed holomorphic 1-differentials. The main result, theorem 2.6, gives a complete description of a (locally split) closed symmetric 2-differential in a neighborhood of a general point of $B_w$. A key feature of theorem 2.6 is that closed symmetric 2-differentials still have a decomposition as a product of 2 closed 1-differentials (in a generalized sense) even at the points of $B_w$. The (possibly multi-valued) closed 1-differentials can have essential singularities along $B_w$, but one still has a control on these essential singularities. The essential singularities come from exponentials of meromorphic functions acquiring poles along the irreducible components of $B_w$ of order bounded by the order of contact of the 2 foliations defined by the symmetric 2-differential along that irreducible component.
Universal spaces for unramified Galois cohomology
2014 · PREPRINT · en
We construct and study universal spaces for birational invariants of algebraic varieties over algebraic closures of finite fields.
Essential dimension, stable cohomological dimension, and stable cohomology of finite Heisenberg groups
2014 · PREPRINT · en
We compare the notions of essential dimension and stable cohomological dimension of a finite group G, prove that the latter is bounded by the length of any normal series with cyclic quotients for G, and show that, however, this bound is not sharp by showing that the stable cohomological dimension of the finite Heisenberg groups H_p, p any prime, is equal to two.
The ambiguity index of an equipped finite group
2014 · PREPRINT · en
In \cite{Ku0}, the ambiguity index $a_{(G,O)}$ was introduced for each equipped finite group $(G,O)$. It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group $G$ assuming that all local monodromies belong to conjugacy classes $O$ in $G$ and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (\cite{Kun1}, see also \cite{BO87}) and hence can be easily computed for many pairs $(G,O)$.
Galois Theory and Projective Geometry
2013 · ARTICLE · en
We explore connections between birational anabelian geometry and abstract projective geometry. One of the applications is a proof of a version of the birational section conjecture.
On stable conjugacy of finite subgroups of the plane Cremona group, I
2013 · PREPRINT · en
We discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We show that the group $H^1(G,Pic(X))$ is a stable birational invariant and compute this group in some cases.
Closed symmetric 2-differentials of the 1st kind
2013 · ARTICLE · en
A closed symmetric differential of the 1st kind is a differential that locally is the product of closed holomorphic 1-forms. We show that closed symmetric 2-differentials of the 1st kind on a projective manifold X come from maps of X to cyclic or dihedral quotients of Abelian varieties and that their presence implies that the fundamental group of X (case of rank 2) or of the complement X∖E of a divisor E with negative properties (case of rank 1) contains subgroup of finite index with infinite abelianization. Other results include: i) the identification of the differential operator characterizing closed symmetric 2-differentials on surfaces (using a natural connection to flat Riemannian metrics) and ii) projective manifolds X having symmetric 2-differentials w that are the product of two closed meromorphic 1-forms are irregular, in fact if w is not of the 1st kind (which can happen), then X has a fibration f:X→C over a curve of genus ≥1.
Collineation group as a subgroup of the symmetric group
2013 · ARTICLE · en
Let Ψ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension ≥ 3 over a field. Let H be a closed (in the pointwise convergence topology) subgroup of the permutation group GΨ of the set Ψ. Suppose that H contains the projective group and an arbitrary self-bijection of Ψ transforming a triple of collinear points to a non-collinear triple. It is well-known from [9] that if Ψ is finite then H contains the alternating subgroup AΨ of GΨ. We show in Theorem 3.1 below that H = GΨ, if Ψ is infinite.
On the irreducibility of Hilbert scheme of surfaces of minimal degree
2013 · ARTICLE · en
The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙ m+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik. S., On Chisini's conjecture II, Izv. Math., 2008, 72(5), 901-913 (in Russian)] for coverings of projective plane branched in a special class of rational curves.
Курсы (0)
Нет курсов.