Interval analysis, Numerical methods with verification, Algebraic properties of intervals, errors, convex bodies, stochastic numbers etc., Hausdorff approximations, Mathematical modeling in biology, enzyme kinetics, microbial growth, synaptic transmission, special relativity.
Software Technologies; Software Quality Requirements; Comparative Analysis; Software Development Models; Software Project Management.
Numerical methods, Approximation theory.
Algebra.
Non-linear elliptic and parabolic equations and systems appearing in geometry, physics and engineering: e.g. the minimum surface equation, the equation of Monge-Ampere, the equation of anisotopic diffusion in the theory image clarification, viscose solutions, diffraction problems of equations with non-continuous coefficients and others.
My scientific interests are in the field of numerical methods for solving differential and integral equations, in particular - the methods of finite differences, finite elements, boundary elements, as well as their application to the mathematical models of physical and industrial processes.
Approximations by rational functions in the complex plane: Pade approximation, best rational approximation, orthogonal polynomials, rate of approximation; complex analysis, potential theory, numerical analysis, mathematical modelling.
General topology (set-valued mappings), Functional analysis.
Differential Equations, Dynamical Systems, Mathematical Physics.
Algebraic geometry: surface theory, Algebra: associative algebras, theory of finite group representations, Artin braid group representations, Combinatorics: census problems. Mathematical Chemistry: isomerism in organic cemistry, Mathematical Economics: sets of preferences, utility functions.
