The Institute of Mathematics offers its customers services for the performance of Research in the field of Algebra 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.

Research areas:

- Anisotropic algebraic groups: multiplicative groups of simple algebras, Whitehead groups, congruence problems;
- Simple algebras: structural problems, classification of such algebras over important special fields;
- Algebraic geometry: Brauer groups and the arithmetic of algebraic varieties;
- Representations of semisimple algebraic groups in positive characteristic: behavior of images of individual elements in representations, restrictions of representations to subsystem subgroups, problems of recognition of representations and linear groups;
- Properties of finite linear groups in characteristic zero related to the structure of their Hall subgroups;
- Application of methods of representation theory and finite group theory to the study of fast matrix multiplication algorithms;
- Algebraic aspects of cryptographic schemes for modular secret sharing.

Key results:

- Results on the structure of involutive Henselian weakly ramified division algebras are obtained, which are then used to prove formulas for computing the reduced unitary Whitehead groups of exterior forms of anisotropic algebraic groups of type An;
- A theory of finite π-soluble irreducible linear groups of arbitrary degree is developed, which provides a solution to the Isaacs problem;
- It is shown that the bilinear complexity of multiplying a 3×2 matrix by a 2×3 matrix is ​​15. The Gaschütz problem is solved;
- Composition factors of restrictions of modular representations of simple algebraic groups to subsystem subgroups of type A1, representations of special linear groups to subsystem subgroups of type A1×A1, and locally small representations of groups of types An, Bn, and Dn to subsystem subgroups of type A1 are described;
- For unipotent elements of prime order, a block structure is defined for their images in modular irreducible p-bounded representations of classical algebraic groups of dimension ≤100.

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

Key advantages.

High scientific level: The Algebra Department is headed by leading scientists whose work on anisotropic algebraic groups is internationally recognized; the institute counts academicians and laureates of prestigious prizes (Lenin and State Prizes).

Applied value: The results are applied in cryptology, optimization, physics, and other fields, solving pressing problems in economics, ecology, and logistics.

International recognition: Collaboration with universities and institutes in Germany, France, the USA, Russia, and other countries; organization of conferences and publications in prestigious journals.

Scientific achievements
Research covers a wide range of modern algebra, algebraic geometry, and number theory, with contributions to global science through the institute's papers and dissertations.

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 Algebraic Research services for application in various fields of science and industry under outsourcing agreement and/or subcontracting/

Partners interested in purchasing Algebraic Research services for application in various fields of science and industry under a distribution services agreement.