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Timashev Dmitrii Andreevich

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Total publications: 8
Scientific articles: 7
Presentations: 32

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Candidate of physico-mathematical sciences (1997)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Website: http://mech.math.msu.su/department/algebra/staff/timashev
Keywords: invariant theory; reductive group; representation; Lie algebra; embeddings of homogeneous spaces; spherical varieties.

Subject:

Main interests lie in the theory of algebraic transformation groups and in Invariant Theory. Spherical homogeneous spaces of reductive algebraic groups were studied, and the theory of equivariant embeddings of arbitrary homogeneous spaces and varieties acted on by a reductive group was developed. A classification of $B$–orbits on a spherical homogeneous space $G/TU'$ was obtained, where $B$ is a Borel subgroup in a connected reductive group $G$, $T$ is a maximal torus in $B$, and $U$ is the maximal unipotent subgroup. The Hasse graph of these orbits was described. The general Luna–Vust theory of equivariant embeddings of homogeneous spaces was reworked and extended to arbitrary $G$–varieties. This work resulted in the classification of $G$–varieties of complexity 1 (i.e. such that a generic $B$–orbit has codimension 1) in terms of combinatorial geometry, which generalizes the classification of toric and spherical varieties. Divisors on normal $G$–varieties were studied. In particular, criteria for a Cartier divisor to be globally generated and ample were given. An integral formula for intersection numbers of divisors on a variety of complexity 1 generalizing Brion's formula for spherical varieties was obtained and applied to computing the degree of an arbitrary 3–dimensional orbit in any $SL(2)$–module. Affine homogeneous spaces of reductive groups such that all their equivariant affine embeddings have finitely many orbits were classified (a joint work with I. V. Arzhantsev). A classification of 2-step nilpotent Lie algebras with the dimensions of the quotients of the lower central series less or equal than $(5,5)$ or $(6,3)$ was obtained (a joint work with L. Yu. Galitski) with the help of invariant-theoretic methods, in particular, Vinberg"s theory of $\theta$–groups.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1993 (department of higher algebra). Ph.D. thesis was defended in 1997.

   
Main publications:
  • Galitski L. Yu., Timashev D. A. On classification of metabelian Lie algebras // Journal of Lie Theory, 1999, 9 (1), 125–156.
  • Timashev D. A. Cartier divisors and geometry of normal G–varieties // Transformation Groups, 2000, 5 (2), 181–204.
  • Arzhantsev I. V., Timashev D. A. Affine embeddings with a finite number of orbits // Transformation Groups, 2001, 6(2), 101–110.

http://www.mathnet.ru/eng/person8841
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/357504

Publications in Math-Net.Ru
1. On differential characteristic classes of metrics and connections
D. A. Timashev
Fundam. Prikl. Mat., 20:2 (2015),  167–183
2. Natural differential operations on manifolds: an algebraic approach
P. I. Katsylo, D. A. Timashev
Mat. Sb., 199:10 (2008),  63–86
3. Equivariant symplectic geometry of cotangent bundles. II
D. A. Timashev
Mosc. Math. J., 6:2 (2006),  389–404
4. Equivariant compactifications of reductive groups
D. A. Timashev
Mat. Sb., 194:4 (2003),  119–146
5. Classification of $G$-varieties of complexity 1
D. A. Timashev
Izv. RAN. Ser. Mat., 61:2 (1997),  127–162
6. $G$-Varieties of complexity 1
D. A. Timashev
Uspekhi Mat. Nauk, 51:3(309) (1996),  213–214
7. Generalization of the Bruhat decomposition
D. A. Timashev
Izv. RAN. Ser. Mat., 58:5 (1994),  110–123

8. Ernest Borisovich Vinberg
I. V. Arzhantsev, S. M. Gusein-Zade, Yu. S. Ilyashenko, A. L. Onishchik, A. B. Sossinsky, D. A. Timashev, M. A. Tsfasman
Mosc. Math. J., 8:4 (2008),  617–620

Presentations in Math-Net.Ru
1. A new proof of Lie's theorem (based on a work by V. P. Burichenko)
D. A. Timashev
Lie groups and invariant theory
March 7, 2018
2. Orbits in real loci of spherical varieties
D. Timashev
Transformation groups 2017. Conference dedicated to Prof. Ernest B. Vinberg on the occasion of his 80th birthday
December 14, 2017 15:30   
3. Real orbits on spherical homogeneous spaces: the split case (based on a joint work with S. Cupit-Foutou)
D. A. Timashev
Lie groups and invariant theory
September 20, 2017 16:45
4. On the school-conference on spherical varieties at Sanya
D. A. Timashev
Lie groups and invariant theory
March 15, 2017 16:45
5. Orbits of a real semisimple Lie group on the real points of a symmetric space
D. A. Timashev
Lie groups and invariant theory
November 16, 2016 16:45
6. Когомологии Галуа редуктивных вещественных алгебраических групп
D. A. Timashev
International conference on algebraic geometry, complex analysis and computer algebra
August 8, 2016 11:30
7. Galois cohomology of real reductive algebraic groups (based on a joint work with M. V. Borovoi)
D. A. Timashev
Lie groups and invariant theory
March 16, 2016 16:45
8. On the conference "Sphericity 2016"
D. A. Timashev
Lie groups and invariant theory
March 2, 2016 16:45
9. Compatible Lie structures on semisimple Lie algebras (based on a paper by A. Panasyuk)
D. A. Timashev
Lie groups and invariant theory
November 26, 2014 16:45
10. On differential characteristic classes of metrics and connections
D. A. Timashev
Lie groups and invariant theory
October 8, 2014 16:45
11. Symplectic manifolds with invariant Lagrangian submanifold
D. A. Timashev
Modern geometry methods
March 19, 2014 18:30
12. Skew-symmetric covariants of a simple Lie algebra with values in the adjoint representation (based on a paper by C. de Concini, P. Papi, C. Procesi)
D. A. Timashev
Lie groups and invariant theory
February 19, 2014 16:45
13. Multiplicities of ideals in local rings and coconvex bodies (based on a paper by K. Kaveh and A. G. Khovanskii)
D. A. Timashev
Lie groups and invariant theory
December 4, 2013 16:45
14. Quotients of affine spherical varieties by unipotent subgroups
Dmitri Timashev
International conference "Algebraic Topology and Abelian Functions" in honour of Victor Buchstaber on occasion of his 70th birthday
June 21, 2013 17:00   
15. On the conference in Israel (continuation of the talk on 13th March)
D. A. Timashev
Lie groups and invariant theory
March 20, 2013 16:45
16. On the conference in Israel
D. A. Timashev
Lie groups and invariant theory
March 13, 2013 16:45
17. Classification of spherical varieties (a survey) (continuation)
D. A. Timashev
Lie groups and invariant theory
November 9, 2011 16:45
18. Classification of spherical varieties (a survey)
D. A. Timashev
Lie groups and invariant theory
November 2, 2011 16:45
19. Hamiltonian varieties with invariant Lagrangian subvarieties (continuation)
D. A. Timashev
Lie groups and invariant theory
September 21, 2011 16:45
20. Hamiltonian varieties with invariant Lagrangian subvarieties (joint work with V. S. Zhgoon)
D. A. Timashev
Lie groups and invariant theory
September 14, 2011 16:45
21. Ветвление для симплектических групп (по работе N. Wallach и O. Yacobi)
D. A. Timashev
Lie groups and invariant theory
December 2, 2009
22. Алгебраические симметрические пространства: схемы Сатаке, классификация и гармонический анализ
D. Timashev
Lie groups and invariant theory
December 10, 2008
23. Подсчет числа точек на однородных пространствах над конечным полем (по работе M. Brion, E. Peyre)
D. A. Timashev
Lie groups and invariant theory
April 9, 2008
24. О конференции в Канаде
D. A. Timashev
Lie groups and invariant theory
October 3, 2007
25. Типовые разделяющие инварианты (по работе M. Domokos)
D. A. Timashev
Lie groups and invariant theory
November 1, 2006
26. Естественные дифференциальные операции на многообразиях: теоретико-инвариантный подход (по совместной работе с П. И. Кацыло)
D. A. Timashev
Lie groups and invariant theory
September 20, 2006
27. Frobenius splitting и его приложения (продолжение)
D. A. Timashev
Lie groups and invariant theory
May 10, 2006 16:20
28. Frobenius splitting и его приложения
D. A. Timashev
Lie groups and invariant theory
May 3, 2006 16:20
29. Многообразия орисфер и эквивариантная симплектическая геометрия кокасательных расслоений
D. A. Timashev
Lie groups and invariant theory
November 17, 2004 16:20
30. Действие группы Вейля на множестве орбит сферической подгруппы в многообразии флагов (по работе N. Ressayre)
D. A. Timashev
Lie groups and invariant theory
September 22, 2004 16:20

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