The Institute of Mathematics offers its customers services for carrying out research in the field of Number Theory and Discrete Mathematics for application in various fields of science and production under an outsourcing agreement and/or subcontracingt and is looking for partners interested in a distribution services agreement.

Fundamental research areas:

- Diophantine approximations of points on smooth manifolds in spaces of various structures and dimensions;
- Estimating the number of integer polynomials with given constraints on the derivative;
- Distribution of algebraic numbers with given characteristics;
- Distribution of roots of random polynomials;
- Application of methods of the metric theory of Diophantine approximations to ill-posed problems of mathematical physics;
- Classification of resonant sets in Diophantine approximation theory and its application to signal extraction in noisy data transmission channels used in antenna devices;
- Optimization problems on permutations and graphs, focusing on linear and quadratic assignment problems, the traveling salesman problem, and graph and hypergraph laying problems. Development of approximate, heuristic, and exact methods for solving these problems, studying polyhedral aspects, and finding effectively solvable cases;
- Enumerative and algebraic combinatorics for graphs and objects of topological and algebraic nature. In particular, enumeration of nonisomorphic maps on surfaces, coverings of topological surfaces and Seifert three-manifolds, non-conjugate subgroups of finitely generated groups, circular graphs, and finite automata. Study of combinatorial sequences and combinatorial identities, including identities of binomial type;
- Research in combinatorial computational geometry. Problems on partially oriented convex sets, including problems of recognition, separation, finding numerical characteristics, comparison of different types of partially oriented convexity, extreme points, and optimization. Development of methods for constructing triangulated surfaces with specified properties in a two-dimensional simplicial complex;
- Research in graph theory: stability and Hamiltonian properties in regular graphs, disjoint subgraph problems in topological and geometric graphs, realization of hypergraphs by graphs with specified properties;
- Metric theory of transcendental numbers: theory of extremal manifolds over real, complex, and p-adic fields, application of the Hausdorff dimension in the theory of Diophantine approximations, estimates for small denominators in ill-posed problems of mathematical physics;
- Number-theoretic algorithms (including primality testing, factorization, discrete logarithm) and applications in cryptology.

Applied research areas:

- Application of methods of the metric theory of Diophantine approximations in the design of radio receiving antenna devices where received signals can be attenuated by white noise;
- Optimization of compression and restoration algorithms for Earth remote sensing (ERS) images with given image parameters;
- Number-theoretic algorithms and their application to building public-key cryptosystems;
- Solving optimization problems in a wide range of subject areas: in the design of telecommunications devices, transport communications, electronic microcircuits, etc.;
- Creating software with pre-specified upper and lower bounds for winning in probabilistic games;
- Using machine learning and artificial neural networks for data processing;
- Solving logistics problems.

Information is posted on the Institute of Mathematics website here. (in Russian)

Research in Number theory and Discrete mathematics at the Institute of Mathematics of the National Academy of Sciences of Belarus offers significant advantages due to its fundamental depth and wide range of practical applications. This work contributes to the development of cryptography, optimization, and data processing, improving the efficiency of technologies in various fields.

Fundamental Advantages.
Developments include Diophantine approximations, the distribution of algebraic numbers, and number-theoretic algorithms such as primality testing and factorization. These results deepen the understanding of mathematical structures and find application in ill-posed problems in physics and transcendental number theory. Publications in specialized journals, such as the "Proceedings of the Institute of Mathematics of the National Academy of Sciences of Belarus," confirm the high academic level.

Applied Advantages.
Number-theoretic methods are used to create public-key cryptosystems and protect information, which is relevant for computer networks. Optimization algorithms solve problems in telecommunications, transportation, integrated circuits, remote sensing image compression, and logistics. Diophantine approximation methods improve radio receiving antennas by recognizing signals in noisy channels.

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 Number Theory and Discrete Mathematics 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 Number Theory and Discrete Mathematics for application in various fields of science and industry under a distribution services agreement.