Sheinman, Oleg KarlovichSteklov Mathematical Institute, Department of Geometry and Topology (leading researcher)
Phone: (095) 938-3787 (office)
The area of main scientific interest: infinite-dimensional Lie algebras (Krichever-Novikov algebras, Lax operator algebras), representation theory, related problems of geometry of moduli spaces and mathematical physics, integrable systems.
Father - Sheinman, Karl Mikhailovich (1926-1996), an aircraft engineer, constructor of
Mother - Sheinman-Topstein, Cecile Yakovlevna (1923-1991), a phylologist, translator of
classical phylosophical works (Plato, Kant, Descartes and others) to Russian.
1966-1971 -- Study in Moscow State University (MSU), Department of Mathematics and
1971 -- Student diploma from the Department of Mathematics and Mechanics of MSU.
Thesis title: "Orbits of the real simplectic group", (Prof. A. A. Kirillov - adviser).
1974-1977 Aspirantura, the Central Institute for Economics and Mathematics of the Academy
1982 Candidate of Science (=PhD) in Physics and Mathematics.
Dissertation title: Duality and subadditive functions in integer linear programming.
2007 Doctor of Science in Physics and Mathematics.
Dissertation title: Krichever-Novikov algebras, their representations and applications in geometry and mathematical physics.
1974 Married, 2 children: the daughter and the son.
1971-1974 A member of staff at the Central Institute for Economics and Mathematics (Moscow),
1977-1995 A member of staff at the Krzhizhanovski Power Engineering Institute (Moscow),
junior researcher, senior researcher
1995-2000 A member of staff at the Institute for Economics of Energetics (Moscow), senior
1993 A member of staff at the Independent University of Moscow
since 2004 a permanent professor of this university
2000 A member of staff at the Steklov Mathematical Institute, leading researcher
1996 RFBR project 96-01-00063 (Head of the project)
1996-98 joint RFBR and DFG project 96-01-00055G (co-Head of the project)
1999-2001 RFBR project 99-01-00198 (Head of the project)
(RFBR=Russian Foundation for Basic Research, DFG=Deutsche Forschungsgemeinschaft)
Since 2002- RFBR projects 02-01-00803, 05-01-00170
Since 2002- Mathematical methods of nonlinear dynamics. The project of the Russ. Acad. Sci.
Lax operator algebras:Introduced in 2006 in the joint work with I.Krichever. Certain basic properties were established there, such as almost graded structure, existense of the almost graded central extensions (the corresponding 2-cocycles are constructed explicitly).The classification of all almost graded central extensions is given in the joint work with M.Schlichenmaier (2007). In my subsequent works I developed certain applications to the theory of integrable systems: the existence and properties of integrable hierarchies.
Krichever-Novikov algebras and their representations:Classification of the coadjoint orbits and its relation to the 21-th problem of Hilbert. Hitchin-Tyurin invariants of Krichever-Novikov algebras. Construction of wedge representations of Krichever-Novikov algebras and their classification by holomorphic bundles on Riemann surfaces. Description of the second order casimirs for the Krichever-Novikov algebras and some more general operators (semi-casimirs). Relation between semi-casimirs, conformal blocks and tangent spaces to certain moduli spaces of Riemann surfaces with marked points and fixed jets of local coordinates. Analog of Weil-Kac formula for characters for the special class of irreducible representations.
2D Conformal Field Theory:Constructing the Conformal Field Theory on moduli spaces of Riemann surfaces with puctures using Krichever-Novikov algebras as algebras of gauge and conformal symmetries. The generalization of the Knizhnik-Zamolodchikov equations on positive genus. Formules for infinitesimal deformation of regular Krichever-Novukov functions and vector fields under deformation of moduli (joint results with M.Schlichenmaier).
Discrete minimization (maximization) problems (1977-82).The duality theory for linear discrete programming. Analog of Kuhn-Tacker theorem for discrete nonlinear programming. Lagrange multipliers for problems in discrete arguments. The extremal properties of subadditive cutting planes.
differential geometry (lectures, seminar; together with I.Krichever)
1995 Riemann surfaces (lectures, seminar; together with O.Schwarzman and
1996-98 Seminar on Lie algebras and their applications (together with I.Paramonova)
2002-03 Basic representation theory
2003-04 Calculus on manifolds
2004 -- Krichever-Novikov algebras and their representations
2008/09 -- Lax operator algebras
2000-present time: Seminar on Riemann surfaces, Lie algebras and mathematical physics
(together with S.Natanzon and O.Schwarzman)
Principal publications: (see the full list of publications here)
Monographs, Textbooks- Current algebras on Riemann surfaces. De Gruyter Expositions in Mathematics, 58, Walter de Gruyter GmbH & Co, Berlin–Boston, 2012, ISBN: 978-3-11-026452-4, 150 pp. - Алгебры Кричевера-Новикова, их представления и приложения в геометрии и математической физике. Совр. пробл. матем., том 10. Москва, МИАН, 2007. 140 стр. - Основы теории представлений. Москва, МЦНМО, 2004, 64 стр. (English translation: Basic representation theory. Moscow, MCCME, 2005). - Задачи семинара "Алгебры Ли и их приложения". Москва, МЦНМО, 2004, 48 стр. (совместно с И.М.Парамоновой).
Scientific Articles- Lax equations and Knizhnik-Zamolodchikov connection. math/1009.4706 - Lax operator algebras and Hamiltonian integrable hierarchies. math/0910.4173 and Uspekhi Mat. Nauk, 2011, no.1, 151-178 (Dedicated to I.Krichever on the occasion of his 60-th Birthday). - Lax operator algebras and integrable hierarchies. Proceedings of the Steklov Math. Institute, v.263, p.216-226 (2008).