Institute for Low Temperature Physics and Engineering

Mathematical division

DEPARTMENT OF MATHEMATICAL PHYSICS

Head of the Department:  Doctor of Sciences KOTLYAROV  Vladimir Petrovich

tel: +(380)-57-341-09-69, 341-09-85
fax: +(380)-57-345-05-93 

E-mail: kotlyarov@ilt.kharkov.ua

Department of Mathematical Physics was founded in 1960. It is headed by Professor V.A.Marchenko from the very beginning to 2001. The staff of the Department consists of 3 Doctors of Sciences (V.A.Marchenko, F.S.Rofe-Beketov, V.P.Kotlyarov) and 6 Candidates of Sciences (S.I.Bezuglyi, L.L.Vaksman, N.I.Nessonov, S.D.Sinelshchikov, M.A.Kudryavtsev, V.M.Kulagin).

Main results of the Department:

• the inverse scattering problem, the inverse spectral problem for the Schrodinger equation with periodic potential;
• the method for solving the wide class of problems of electromagnetic wave diffraction on periodic structures;
• the new approach to constructive solving the inverse spectral problems for the differential operators with non-decreasing coefficients and its applications to constructing new classes of solutions of nonlinear evolution equations;
• the quantum group theory and its applications to the problems of quantum field theory and geometry;
• new field of investigations in algebraic number theory, D-modules and conformal field theory;
• theory of completely integrable differential equations related to affine Lie algebras;
• the Poisson-Lie group theory and the classification of solutions of the classical Yang-Baxter equation;
• the theory of cocycles of dynamical systems and their applications to classification of different group actions on the space with measure;
• the structure of the Neumann algebras and their automorphisms and its application to studying the non-commutative entropy in the statistical physics models.

The main results of the Department was published in the books:

1. Z.S.Agranovich and V.A.Marchenko, Inverse scattering theory, Kharkov University,1960.
2. V.A.Marchenko, Spectral theory of the Sturm-Liouville operators, Kiev, Nauk.Dumka, 1972.
3. V.A.Marchenko and E.Ya.Khruslov, Boundary value problems in domains with fine-grain boundary, Kiev,Nauk.Dumka, 1974.
4. V.A.Marchenko, Sturm-Liouville operators and applications, Kiev, Nauk.Dumka, 1977; English translation: Birkhauser Verlag, 1985.
5. L.L.Vaxman and M.S.Lifshits, Nonselfadjoint commuting operators in Hilbert space,Berlin: Springer, Lecture Notes in Mathematics, 1987.
6. V.A.Marchenko, Non-linear equations and operator algebras, Kiev, Nauk.Dumka, 1986; English translation: D.Riedel, Dordrecht, 1987.
7. V.A.Marchenko and E.Ya.Khruslov. Homogenized models of microinhomogeneous media. Kiev, Naukova Dumka 2005.
8. V.A.Marchenko. Introduction to a theory of inverse spectral analysis. Acta, Kharkov, 2005.

The works of the Department are well known in the world, that was testified by the Lenin Prize (V.A.Marchenko, 1962), N.N.Krylov's Prize of the Academy of Science of Ukraine (V.A.Marchenko, 1982), the Prize of the Academy of Sciences of the Soviet Union (V.G.Drinfeld, 1988), the State Prize of Ukraine (V.A.Marchenko, 1989), the Fields Gold Medal (V.G.Drinfeld, 1990).

The co-workers of the Department participate in international scientific projects such as the long-time International Science Foundation project , INTAS projects of European Community, CRDF and STCU.