Algebra (theory of radicals, structural problems in algebraic systems near to rings, modules and algebras);
Quasigroups and combinatorial analysis (general theory of quasigroups and algebraic operations, combinatorial problems in quasigroups and coding and ciphering information applications);
Mathematical logic (algorithmic problems of functional expressivity as well as its generalizations into non-classical logics);
Topological algebra;
Geometry of discrete groups;
The quality theory of differentiated equations and the theory of algebraic invariants;
Applying group analysis and Lie algebras to differentiated equations;
Functional analysis.
Mathematical modeling;
Numeric methods;
Probability theory;
Game theory and optimal control;
Modeling of economic processes.
Computer science
Theoretical basics of computer science (formal models of computation, grammars and formal languages, computational algebra);
Processing of natural language;
Modeling and simulation systems;
Technology of program product development (methods, advanced means of development of programming system, methodologies and integrated technologies for the development of program products, processing systems of non-structured data).
Theoretical and applied research in the area of information systems (Theoretical research: algorithms and new technologies for acquisition, formalization and management of knowledge; ultrasound image processing. Applied research: decision support systems, computer assisted intelligent systems for training, web content management systems).