МЕГАГРАНТЫ

Лаборатория алгебраической геометрии и ее приложений

О лаборатории

Наименование проекта Алгебраическая геометрия и ее приложения

Ссылка на официальный сайт

№ договора:
11.G34.31.0023

Наименование ВУЗа:
ГОБУ ВПО "Государственный университет - Высшая школа экономики"

Область научных исследований:
Математика

Цель проекта:
Получение новых результатов в алгебраической геометрии, комплексной геометрии и дифференциальной геометрии

Основные задачи проекта:
1. Доказательство существования рациональных кривых и рациональных точек на поверхностях типа К3;
2. Доказательство глобальной теоремы Торелли и ее применение для изучения геометрии и топологии гиперклеровых многообразий;
3. Изучение мотивных структур, возникающих в некоммутативной геометрии;
4. Исследование частных случаев гомологичной зеркальной симметрии;
5. Исследование мотивного применения циклических космологий в контексте некоммутативной гипотезы Тэйта.

Ведущий учёный

vu mini 23 

ФИО: Богомолов Федор Алексеевич

 

Ученые степень и звание:
Доктор физико-математических наук, профессор.

Занимаемые должности:
Профессор Института математических наук Куранта в Нью-Йорке; научный руководитель Лаборатории алгебраической геометрии и ее приложений Национального исследовательского университета высшей школы экономики.

Области научных интересов:
1. Алгебраическая геометрия.
2. Теория чисел и их представлений.

Основные научные достижения:
Работает преимущественно в области алгебраической геометрии. К основным трудам относятся, в частности, исследования в области Калаби-Яу многообразий и стабильных расслоений. Важное место в работах ученого посвящено взаимодействию современной алгебраической геометрии с теорией струн.

Научное признание:
- почетный участник нескольких международных конференций, в том числе организованных Институтом коммерческого управления (1978 г.) и Институтом общественных наук Тата (1991, 1992 гг.);
- организатор или член оргкомитета ряда конференций по алгебраической геометрии, включая конференции в Ярославле, (1979, 1983, 1987 гг.), конференции Института теоретической и прикладной математики в США (1998, 2001, 2003 гг.) и ряда других;
- член редколлегий ведущих международных научных журналов, в том числе “Geometric and Functional Analyses” (c 1995 г.), “Central Europian Journal Of Mathematics” (c 2001 г.), с 2009 г. - главный редактор этого журнала.
- автор более 100 статей по математике;
- автор или редактор 7 книг и записок лекций по различным областям алгебраической геометрии;
- руководит научной работой 13 аспирантов, 9 из которых обучаются в Институте математических наук Куранта.

1. The action of circumference on smooth odd-dimensional spheres, Mathematicheskie
Zametki 1969 v 5 (4) p. 401-407 (English Translation p.241-244).
2. On varieties with trivial canonical class, Uspechi Math. Nauk 1973 v 28 (6) p.103-104
(English translation. Russian Math. Surveys p.193-194).
3. Kahler manifolds with trivial canonical class, Izvestya AN SSSR ser.matem. 1974 v
38 (1) p.11-21, (English translation Math USSR Izvestya 1974 v 8 (1) p.9-20).
4. On decomposition of Kahler Varieties with trivial canonical class, Math. Sbornik
1974 v 93(135) (4) p. 573-583 (English translation Math. USSR Sbornik v 22(1)
p.580 -583).
5. Compact Kahler varieties, Ph.D. Thesis, Steklov Institute of Math. 1973 p 1-67.
6. Coherent states (jointly with M.I.Monastyrski), preprint ITEP 1976 p 1-25.
7. Classification of surfaces of class 70 with b2 = 0, Izvestya AN SSSR 1976 v 40 (2)
p.273 - 288 (English translation Math USSR Izvestya 10 (2) p.255 - 269).
8. Families of curves on surfaces of general type, Doklady AN SSSR 1977 v 236 (6) p.
1294 - 1297 (English translation Soviet Math.Doklady p.1041 -1044).
9. Holomorphic tensors and vector bundles, Izvestya AN SSSR 1978 v 42 (6) 1227 - 1287
(English translation Math USSR Izvestya 1979 v 13 (1) p 499 -544).
10. Symmetric tensors, Uspechi Math Nauk 1978 v 33 (5) p.171 - 172 (English translation
Russian Math.Surveys 33 Part 2 p.179-180).
11. Unstable vector bundles on curves and surfaces, ICM-78 Proccedings Helsinki p.517 -
524.
12. Invariant theory and vector bundles (summer school C.I.M.E. 1977), Algebraic surfaces
III Proceedings of C.I.M.E. Italy 1981.
13. Hamiltonian Kahler varieties, Doklady AN SSSR 1978 v 243 (5) p.1101- 1104 (English
translation Soviet Math. Doklady v 19 (6) p.1462 - 1465).
14. Converse Galois problem, Max Planck Institute preprint 1979 p 11 - 14 Arbeitstagung
1979.
15. Kahler manifolds with trivial canonical class, Preprint Institute des Hautes Etudes
Scientifiques 1981 p.1 -32.
16. Sur l‘algebricite des representation l-adique, Comptes Rendus Academy des Science
Paris 1980 v 290 p.701 - 703.
17. Points of finite order on abelian varieties, Izvestya AN SSSR 1980 v 44 (4) p. 782 -
804 (English translation Math.USSR Izvestya 1981 v 17 (1) p.55 -72).
18. Surfaces of class 70 and affine geometry, Izvestya AN SSSR 1982 v 46 (4) p. 742 -
783) (English translation Math USSR Izvestya 1983 v 21 (1) p 31 -73).
19. Analytic sections of conic fibrations, Trudy MIAN 1984 v 169 p.16-23.
20. Stable rationality of the quotient spaces for simply-connected groups, Math.Sbornik
1986 v 130 (1) p 3-17.
21. Rationality of some quotient spaces (jointly with P.Katsylo), Math.Sbornik 1985 v
126 (4) p. 584 -589.
22. On decomposition of cohomology classes, Amsterdam University Preprint 1985 R7/20.
23. Rationality of the moduli spaces of hyperelliptic curves of arbitrary genus, Proceedings
of Canadian Math. Society 1986 Publ 6 p 17-37.
24. Brauer groups of the quotient spaces of linear representations Izvestya AN SSSR 1987
v 51 (3) p.485-515.
25. 2-cocycles and Azumaya algebras under birational transformations of algebraic schemes
(jointly with A.Landia ), Compositio Math. 1990 v 76 p 1-5.
26. Geometry of the spaces of orbits phases for 3He and neutron star (jointly with
M.I.Monastyrski ), Theoretical and Mathematical Physics 1987 v 73 p.210-222.
27. On stable cohomology and rationality problem, Max Planck Institute preprint 1986
p.17 - 21 Arbeitstagung 1986.
28. Brauer groups of the fields of invariants of algebraic groups, Math.Sbornik 1989 v 180
(2) p.279-299.
29. Abelian subgroups of the Galois groups, Izvestya AN SSSR 1991 v 55 (1) p.32-67
(English translation Math. USSR Izvestiya 1992 v 38 (1) p.27–67).
30. On two conjectures in birational algebraic geometry, Satellite ICM-90 Conference
Proceedings Algebraic Geometry and Analytic Geometry Springer Verlag 1991 p.26
-52.
31. Instantons and Mirror K3 surfaces (jointly with P.Braam ), Com. in Math.Physics
1992 v 143 (3) p.641 -646.
32. Stable cohomology of groups and algebraic varieties, Math.Sbornik 1992 v 183 (5) p
1- 27 (English translation Russian Acad Sci.Sb. Math. 1993 v. 76 (1) p.1–21).
33. Stability of vector bundles on surfaces and curves, Taniguchi conference (December
90 ) Proceedings “Einstein Metrics and Yang-Mills connections” Marcel Dekker ,Inc
1993 p.35 -49.
34. Tensors in algebraic geometry, in Developments in Mathematics:The Moscow school
Editors V.Arnold, M. Monastyrski Chapman and Hall 1992 London ,Glasgow,New
York, p.34-53.
35. Commuting elements in the Galois groups, Schriftenreine Heft Nr 173 1993 Kaiserslautern.
36. Fillability of contact pseudoconvex manifolds, Gottingen University Preprint 1993
Heft 13 p 1 -13.
37. On the diameter of plane algebraic curves, Mathematical Research Letters 1994 v 1 p
95-98.
38. Stable vector bundles on algebraic surfaces, Math. Sbornik 1994 v 185 (4) p 3-26.
39. On the structure of the Galois groups of the fields of rational functions, Proceedings
of Symposia in Pure Mathematics Volume 58.2(1995) (S.Barbara conference 1992 “
K-theory and quadratic forms “) p.83–88.
40. Geometric properties of curves defined over number fields, (jointly with D.Husemoller)
University of Maryland preprint 1993 (to appear in Einseignement Mathematique).
41. Linear tori with the action of finite groups, (in russian) Mathematical Notes v. 57 N
5 (1995) p. 643-652.
42. On the cohomology ring of simple Hyperkahler manifold, Geometric and Functional
Analysis (GAFA )v 6 N 4 1996 p.612 -618.
43. Weak Hironaka Theorem (jointly with T. Pantev), Mathematical Research Letters v.3
1996 p. 299-308.
44. On Guan examples of simply connected non-kahler compact complex manifolds, American
J. of Mathematics v.118 N 5 1996 p.1037-1046.
45. Stein small deformations of strictly pseudoconvex surfaces (jointly with Bruno de
Oliveira), Contemporary Mathematics v 207 1996 pp.25-41.
46. Complex manifolds and algebraic foliations, RIMS-1084 preprint 1996 pp.1-5.
47. Projective Surfaces and Infinite groups (jointly with L.Katzarkov), Geometric and
Functional Analysis (GAFA) v 8 N 2 (1998) p.243-272.
48. Symplectic four manifolds and projective surfaces (jointly with L.Katzarkov), Topology
and its applications v 88 (1998) p. 79-109.
49. Infinite groups in projective and symplectic geometry ( jointly with L.Katzarkov) (
London Math. Soc. Lect. Note Series 260, 85-123 (1999))
50. Vanishing theorems and universal coverings of projective varieties, alg-geom e-print
9808103 (to appear in The Asian Journal of Mathematics).
51. On the density of rational points on elliptic fibrations, (jointly with Yu. Tschinkel)
Journ. Reine und Angew. Math., 511, 87-93, (1999).
52. Density of rational points on Enriques surface, (jointly with Yu. Tschinkel) Math.
Res. Letters, 5, p. 623-628, (1998).
53. Symplectic Lefschetz fibrations with arbitrary fundamental groups (jointly with
J.Amoros, L.Katzarkov,T. Pantev) Journal of Diffrential Geometry , v 54(2000) N
3 pp.489-545
54. Density of rational points on elliptic K3-surfaces, (jointly with Yu. Tschinkel), Asian
Journal of Mathematics v.4 N 2 pp.351-368 (2000) .
55. Geometric properties of curves defined over number fields (jointly with D.Husemoller),
Max Planck Institute Preprint (2000).
56. Monodromy of elliptic surfaces, (jointly with Yu. Tschinkel), 22 pp.,in ”Galois groups
and Fundamental Groups” MSRI Publication v 41 Cambridge University Press 2003
pp. 167 - 181.
57. Lagrangian subvarieties of abelian fourfolds, (jointlywith Yu. Tschinkel ),Asian Journal
of Mathematics v.4 N 1 p.19-36 (2000)
58. Hyperelliptic Szpiro Inequalities (jointly with L.Katzarkov,T.Pantev), JDG 2002 v 61
pp 51–80
59. Singularities on complete algebraic varieties (jointly with Bruno de Oliveira), preprint
(2000).
60. Commuting elements in Galois groups of function fields (jointly with Yu. Tschinkel )
”Motives,Polylogarithms and Hodge theory” editors :Fedor Bogomolov,Ludmil Katzarkov
International Press Lecture Series Vol 3 p 1 p. 75-114 (2002)
61. Rationality of moduli of elliptic fibrations with fixed monodromy (jointly with T.
Petrov ,Yu. Tschinkel ) GAFA 2002 vol 12 N 6 p.1105-1156
62. Reconstruction of function fields (jointly with Yu. Tschinkel ) math.AG/0303075
submitted to GAFA
63. Rational Curves on Foliated Varieties (jointly with M.McQuillan) IHES preprint 27
p. 2000
64 Alterations and resolution of singularities , Book Review (jointly with Yu. Tschinkel
) AMS Bulletin v 39 N1 2001 pp 95–100
65 Simple examples of symplectic Four-manifolds with exotic properties (jointly with Yu.
Tschinkel ) Acta Applicandae Mathematica v.75 (2003) pp.25–28
66 Unramified correspondences (jointly with Yu. Tschinkel ) Contemporary Mathematics
v.300 pp. 17 –25 (2002)
67 On curves correspondences (jointly with Yu. Tschinkel ) Communications in Arithmetic
Fundamental Groups june 2002 pp.157-166
68 Algebraic Curves and One-Dimensional Fields AMS CIMS Lecture Notes N 8 (2002)
(jointly with T.Petrov)
69 Unramified Brauer Groups of Finite simple groups of Lie type Al (jointly with J.Maciel
and T.Petrov) American Journal of Mathematics Vol 126, no. 4, pp. 935–949,2004
70 Special elliptic fibrations (jointly with Yu. Tschinkel ) Fano conference 2002 Proceedings
Publication Universita Degli Studi di Turina 2004 p 223-235
71 Rational curves and points on K3-surfaces (jointly with Yu. Tschinkel ) American
Journal of Mathematics v 125( 2005) p 825-835
72 Curves on abelian varieties over finite fields. (jointly with Yu. Tschinkel) International
Mathematics Research Notices 2005 n 4 p 233-238
73 Vanishing theorems for negative vector bundles on projective varieties and the convexity
of coverings. (jointly with Bruno de Oliveira) Journal of Alegbraic Geometry
2006 v 15 pp 207-222
74 ”Holomorphic functions and vector bundles on coverings of projective varieties” (jointly
with Bruno de Oliveira) Asian Journal of Mathematics 2005 v 9 N 3 pp 295-314
75 Hyperbolicity of nodal hypersurfaces (jointly with Bruno de Oliveira) Crelle Math
Journal 2006 v 596
76 ”Minimal and Maximal Curves” (jointly with Yu. Tschinkel ) Geometric Methods in
Algebra and Number Theory Fedor Bogomolov ,Yuri Tschinkel editors Birkhaeuser
Progress in Mathematics, Volume 235 (2004) pp 43-57
77 Placement of Singularities (jointly with Bruno de Oliveira and Paolo Cascini) Central
European Journal of Mathematics 2006 v 4 N 2 p 194- 208
78 Algebraic varieties over small fields (jointly with Yu. Tschinkel ) Proceedings ”Diophantine
Geometry” (Pisa, Centro De Giorgi, April - July 2005)
79 ” Symmetric tensors and the geometry of subvarieties of PN. (jointly with Bruno de
Oliveira) GAFA 2008
80 ”Stable cohomology of finite and profinite groups” p 20-49 in ”Algebraic groups” 2005
Gottingen University
81 Stable cohomology of finite groups MPI Arbeitstagung 1986
82 ”Reconstruction of function fields,” ((jointly with Yu. Tschinkel ) GAFA 2008 p
400-462
83 ”Milnor K2 and Field Homomorphisms” (jointly with Yu. Tschinkel ) Surveys in
Differential Geometry, 2009 Volume 13.
84 Nonramified cohomology of finite simple groups (jointly with Tihomir Petrov and Yuri
Tschinkel) in Progress in Mathematics v 242 Birkhauser Boston 2009
85 ”Co-fibered products of algebraic curves” (jointly with Yu. Tschinkel ) Central European
Journal of Mathematics, Volume 7, Number 3, 2009, pages: 382-386
86 ”On a theorem of Tate” (jointly with Yu. Tschinkel ) CENTRAL EUROPEAN JOURNAL
OF MATHEMATICS, Volume 6, Number 3 / September 2008.
87 ”Ordinary reduction of K3 surfaces” (jointly with Yu. Zarhin ) CENTRAL EUROPEAN
JOURNAL OF MATHEMATICS, Volume 7, Number 2 / June, 2009.
88 Torelli theorem over finite fields (jointly with Yu. Tschinkel and M. Korotiaev ) Pure
and Applied Mathematics Quarterly (PAMQ) Vol. 6.1 2009
89 Coverings of surfaces have infinite type (jointly with Bruno de Oliveira)
90 Stabilization conjecture (jointly with Yu. Tschinkel ) preprint

Back to top