V. N. Karazin Kharkiv National University (Official Site)

Scientific cooperation of the School of Mechanics and Mathematics with scientists from higher educational institutions and research institutes of Ukraine, CIS countries, and far-abroad countries contributes to ensuring a high level of expertise of our alumni.

Science, Branches

Scientists of the School of Mechanics and Mathematics have the most significant achievements in various fields of mathematics; they are founders of many scientific schools in Kharkiv, Kyiv, St. Petersburg, and other cities. Today each Department of the School of Mechanics and Mathematics conducts various kinds of research in several fundamental areas, an outline of a few of them follows.

The Department of Geometry (acting Head of the Department: Corresponding Member of the National Academy of Sciences of Ukraine O. Yampolskyi) conducts research in several new areas: geometry of submanifolds of Finsler spaces, mean curvature flows, the geometry of foliations and distributions, harmonic maps and Grassmann image in Lie groups, the geometry of submanifolds in the Heisenberg group, geometry «in general» in standard three-dimensional geometries.

Research at the Department of Mathematical Physics and Calculus Mathematics (headed by Corresponding Member of the National Academy of Sciences of Ukraine I. Chuieshov) primarily focuses on: nonlinear problems of mathematical physics and qualitative theory of infinite-dimensional dynamical systems, numerical methods in singular and hypersingular integral equations of electrodynamics and theory of diffractions, problems of continuum mechanics and electrodynamics.

At the Department of Differential Equations and Control (headed by Full Professor V. Korobov) the areas of scientific interest are: a general theory of the analytical solution of the problem of acceptable positional control synthesis with control constraints and its derivatives to the given order which is based on the controlled function method and is further development of Lyapunov direct method, the problem of Markov’s moments at the minimum possible interval and its application in the optimal control theory, the problem of nonlinear controlled systems mapping on linear controlled systems, the problem of dynamic systems controllability and stabilization, control of Tymoshenko beam mode, algebraic methods in the theory of nonlinear controlled systems.

Research at the Department of Mathematical Analysis (headed by Full Professor V. Hordevskyi) is focused on: complex and convex analysis, the theory of subharmonic functions, growth and distribution of values of entire and meromorphic functions, mathematical and statistical physics, different classes of differential equations including nonlinear integrodifferential equations with a retarded argument in Banach spaces, ergodic dynamical systems in partial derivatives.

The Department of Mathematical Modeling and Software (headed by Full Professor A. Rutkas) carries out research in: mathematical modeling of the evolution of physical and financial and economic systems, application of spectral analysis and probabilistic statistical methods, the theory of functional differential, impulse and difference equations of Sobolev type, operator sheaf spectral theory.

The scientific interests of the Department of Theory of Functions and Functional Analysis (headed by Full Professor S. Favorov) lie in: theory of analytic functions, the analytic theory of probabilities, the geometry of Banach spaces, algebra.

Areas of scientific interest at the Department of Theoretical and Applied Mechanics (headed by Associate Professor N. Kizilova) are: modeling of environments with complicated properties in electromagnetic fields, hydromagnetic phenomena, balance state and stability of forms of free liquid surfaces that are being magnetized and polarized and of solids levitating in the electromagnetic field, dynamics of shock waves, properties of nanolayer functional coatings, the flow of liquids in the environment (river beds, ecosystems), modeling of the arterial, locomotive and dental human body systems, thermodynamics of biological growth, long-range transport of liquids in plants and animals, biotermohydromechanics, optimum biomechanical systems.

At the Department of Higher Mathematics and Information Science (Associate Professor V. T. Lysytsia acting for the head of the department), research mainly focuses on: model representation of nonlinear nonselfadjoint and non-unitary operators and their application, the theory of stochastic processes, spectral properties of stochastic processes, in particular, methods of solving problems of mathematical physics, the theory of nonlinear oscillations, inverse problems, the theory of diffraction, the problem of computational mathematics and electrodynamics, geometry of manifolds and submanifolds, Hamilton systems with closed trajectories.

The Department of Theoretical and Applied Information Science (headed by Full Professor H. Zholtkevych) centers its scientific explorations on mathematical and computer modeling and its application in software development and research of information and communication, natural and socio-economic systems, mathematical logic, the theory of calculability and its application in the theory of programming and formal software verification, soft computing and its applications in mathematical statistics and software engineering, quantum information science.

At the end of the 4th year of training, students defend their Bachelor’s degree qualification papers. Bachelor’s degree holders are enrolled in Master’s programs based on the results of the competition where their academic performance during the past 4 years and the Bachelor’s diploma are taken into consideration. Both graduates of the School of Mechanics and Mathematics and graduates of any other higher educational institution having diplomas in Mathematics, Information Science, Applied Mathematics can apply for admission to a Master’s program. The departments preparing Masters in the corresponding specialty provide teaching of special courses and supervise diploma papers throughout the entire term of studies.