The Institute of Mathematics offers its customers services for the performance of Research in the field of Functional Analysis and Dynamic Systems for application in various fields of science and production under an outsourcing agreement and/or subcontracting and is looking for partners interested in a distribution services agreement.

Fundamental research areas:

- Functional analysis (geometry of Banach spaces, theory of rearrangement-invariant spaces and Banach lattices, interpolation and extrapolation of spaces and operators, perturbation theory of linear operators, noncommutative functional analysis, C*-algebras);
- General topology (topologies generated by order, topological methods in functional analysis, probability theory, combinatorics, data analysis);
- Probability theory (probabilistic methods in functional analysis, matrix analysis, and graph theory, random matrices, random operators, moment problems);
- Matrix theory (spectral theory of matrices, structured perturbations of matrices, Lyapunov stability, robust stability, matrix spectral localization problems, inequalities for matrix minors);
- Multivariate analysis (special properties of multidimensional matrices and multilinear forms, multidimensional extremum problems)
- Dynamic systems (ergodic theory, spectral and entropy analysis of dynamic systems, limit theorems).

Applied research areas:

- Statistical theory of machine learning (application of analytical and probabilistic methods to evaluate the learning ability of machine learning algorithms, dimensionality and complexity of functional systems);
- Data analysis (application of methods of functional analysis, probability theory, mathematical statistics, and topology to data analysis);
- Mathematical justification of applied heuristics (including artificial intelligence, computer algorithms, engineering designs, etc.);
- Mathematical models of biology (matrix models in evolutionary biology, population dynamics, biological designs in artificial intelligence, genetic algorithms);
- Mathematical models for quantum computing (the Ising model, spin glass dynamics, energy distribution in the Kirkpatrick-Sherrington model).

The information is available on the Institute of Mathematics website here. (in Russian)

Research in functional analysis and dynamical systems at the Institute of Mathematics of the National Academy of Sciences of Belarus is conducted in a specialized department. This research combines fundamental and applied aspects, ensuring its high relevance and practical value.

Fundamental Strengths.
The department focuses on the geometry of Banach spaces, the ergodic theory of dynamical systems, matrix theory, and probabilistic methods, enabling the solution of complex theoretical problems. These areas contribute to the development of general topology, noncommutative analysis, and spectral analysis of systems.

Applied Strengths.
The research is applied in machine learning (algorithm complexity assessment), data analysis, biological models (population dynamics, genetic algorithms), and quantum computing (the Ising model). This provides a mathematical foundation for AI, heuristics, and engineering solutions.

Practical Relevance.
The results are used in statistical machine learning theory, optimization in biology, and data analysis using topology and probabilities, improving the efficiency of applied technologies. Such work is supported by government programs and foundations, fostering innovation.

Institute Activities.

The Institute of Mathematics includes thematic departments and laboratories:
1.Algebra. (in Russian)
2.Computational mathematics and mathematical modeling. (in Russian)
3.Differential equations. (in Russian)
4.Nonlinear and stochastic analysis. (in Russian)
5.Number Theory and Discrete Mathematics. (in Russian)
6.Functional Analysis and Dynamic Systems. (in Russian)

The Institute maintains active creative ties with leading scientific institutions in many countries (Germany, France, Belgium, Russia, Georgia, Ukraine, Greece, Italy, Poland, Austria, China, USA, Great Britain, Denmark, Switzerland, Czech Republic, Yugoslavia, Japan, Bulgaria), and organizes several international conferences, schools, and symposia.

The achievements of the institute’s scientists were recognized by the Lenin Prize (1978), the USSR State Prize (1970, 1972), the BSSR State Prizes (1974, 1978, 1982), the Republic of Belarus State Prize (1998, 2000, 2004), the USSR Council of Ministers Prize (1986), the Lenin Komsomol Prize (1970, 1987) and the Lenin Komsomol of Belarus (1976, 1984, 1990), and the National Academy of Sciences of Belarus Prizes (1993, 1995).

Consumers interested in purchasing services for the performance of Research in the field of Functional Analysis and Dynamic Systems for application in various fields of science and industry under outsourcing agreement and/or subcontracting.

Partners interested in purchasing services for the performance of Research in the field of Functional Analysis and Dynamic Systems for application in various fields of science and industry under a distribution services agreement.