**Sheinman,
Oleg Karlovich**

and Independent University of Moscow (permanent professor)

**Phone:** (095) 938-3787 (office)

**Email:** __sheinman@mi.ras.ru__

__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.

Vita and
Education

Employment

Projects

Learned
Bodies

Principal
Scientific Results

Teaching
at the Independent University of Moscow

Publications

Selected talks

Born:

Father - Sheinman, Karl Mikhailovich (1926-1996), an aircraft engineer,
constructor of

nozzles.

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

Mechanics,

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

of Sciense

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.

**Employment:**

1971-1974 A member of staff at the Central Institute for Economics and Mathematics
(Moscow),

junior researcher

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

researcher

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

**Projects**

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.

**Learned
Bodies:**

The

__Lax operator algebras:__

__Krichever-Novikov
algebras and their representations:__

__2D
Conformal Field Theory:__

__Discrete
minimization (maximization) problems (1977-82).__

**Teaching
at the Independent University of Moscow**

1993/94
differential geometry (lectures, seminar; together with I.Krichever)

1995
Riemann surfaces (lectures, seminar; together with O.Schwarzman and

A.Kulakov)

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**

**Scientific
Articles**

In English In Russian - On certain current algebras related to finite-zone integration. Geometry, topology and mathematical physics. S.P.Novikov's seminar 2006-2007. Ed. by V.M.Buchstaber and I.M.Krichever. AMS Transl. Ser.2, v.224 (2008). - Lax operator algebras. Funct. Anal. and Applications, v.41, no.4, p.46-59 (2007). math.RT/0701648 (joint work with I.M.Krichever) - Projectively flat connections on the moduli space of Riemann surfaces and Knizhnik-Zamolodchikov equations. Proceedings of the Steklov Mathematical Institute, "Nonlinear dynamics", v. 251. ( postscript file in Russian). - Krichever-Novikov algebras and their representations. Proceedings of the conference "Noncommutative geometry and representation theory in mathematical physics", Karlstad, Sweden, 4-11 July 2004. Contemp. Math., 391, p. 313--321. Amer. Math. Soc., Providence, RI, 2005. - Knizhnik-Zamolodchikov equations for positive genera (joint work with M.Schlichenmaier). Uspekhi Mat.Nauk(=Rusian. Math. Surv.), 2004, n 4, p.147-180.(ArXiv: The Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras, II. math.AG/0312040) - Affine Krichever-Novikov algebras, their representations and applications. In: Geometry, Topology and Mathematical Physics. S.P.Novikov's Seminar 2002-2003, V.M.Buchstaber, I.M.Krichever, eds. AMS Translations (2) 212, p.p. 297-316. Math.RT/0304020 - Second order casimirs for the Krichever-Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$. Moscow Mathematical Journal 1(4) 2001; math.RT/0109001 - The fermion model of representations of the affine Krichever-Novikov algebras. Funkt. Anal. Prilozh., 35 (3)2001, 60–72; math.RT/0204178. - Krichever-Novikov algebras and self-duality equations on Riemann surfaces. Uspekhi Mat.Nauk, v.56, No. 1 (2001) (postscript file in Russian . - The Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras. Russian. Math. Surveys, v.54, N 1, p. 213-249 (1999) (translation from: Uspekhi Mat.Nauk, v.54, No. 1, p. 213-250 (1999)) (joint work with M. Schlichenmaier); math.QA/9812083 - Orbits and representations of Krichever-Novikov affine-type algebras. Journal of Mathematical Sciences, 1996, 82, No. 6, 3834-3843 - Sugawara construction and Casimir operators for Krichever-Novikov algebras. Journal of Mathematical Sciences, 1998, 92, No. 2, 3807- 3834; also: Mannheimer Manuskripte Nr. 201 and q-alg/9512016 (joint work with M. Schlichenmaier) - Highest weight modules for affine Lie algebras on Riemann surfaces. Funct. Anal. Appl. 29, No.1, 44-55 (1995) (translation from: Funkt. Anal. Prilozh., 29, No.1, p. 56 -71, (1995). - Representations of Krichever-Novikov algebras. In: Topics in topology and mathematical physics (Novikov, S.P., ed.), Amer. Math. Soc. Translations, Ser.2, Vol.170, p.185 -198, R.I., U.S.A., 1995 - Krichever-Novikov algebras and CCC-groups. Russian Math. Surveys 50, No.5, 1097-1099 (1995) (translation from: Uspehi Mat. Nauk, 50, No.5 253 -254 (1995)). - The orbits and representations of Krichever-Novikov algebras of affine type. In: International Congress of Mathematicians, Abstracts, short communications, p.82. Zurich, 1994. - Affine Lie algebras on Riemann surfaces. Funct. Anal. Appl. 27, No.4, 266-272 (1993) (translation from: Funkt. Anal. Prilozh. 27, No.4,54-62 (1993)) - Highest weight modules over certain quasigraded Lie algebras on elliptic curves. Funct. Anal. Appl. 26, No.3, 203-208 (1992) (translation from: Funkt. Anal. Prilozh. 26, No.3, 65-71 (1992)) - Elliptic affine Lie algebras. Funct. Anal. Appl. 24, No.3, 210-219 (1990) (translation from: Funkt. Anal. Prilozh. 24, No.3, 51-61 (1990))

In English In Russian - Hamiltonian string formalism and discrete groups. Funct. Anal. Appl. 23, No.2, 124-128 (1989) (translation from: Funkt. Anal. Prilozh. 23, No.2, 49-54 (1989)). - Kernel of evolution operator in the space of sections of a vector bundle as integral over trajectories. Funct. Anal. Appl. 23, No.2, 124-128 (1989) (translation from: Funkt. Anal. Prilozh. 23, No.2, 49-54 (1989)). - Dedekind \eta-function and indefinite quadratic forms. Funct. Anal. Appl. 19, No.3, 232-234 (1985) (translation from: Funkt. Anal. Prilozh. 19, No.3, 80-81 (1985)). Lax operator algebras: unexpected outcome, and a new tool of the theory of integrable systems. Southeast Lie theory workshop. College of Charleston, Charleston, SC, USA, December 16-18, 2012.