The most significant scientific and applied results include:
- Practical results in classifying the varieties of universal algebras based on the structure of their skeletons (A. G. Pinus, Ya. L. Mordvinov); - Creation and development of the conditional terms theory ; Applications of this theory results in universal algebra, theory of computation, graph theory (A. G. Pinus, S.V. Zhurkov);
- Research into the derived structures of universal algebras; New approaches to algebraic geometry of universal algebras (A. G. Pinus);
- Description of the rigid classes of non-associative algebras, group algebras, Lie algebras; Establishing the relationship between the theory of algebraic varieties desingularization and theoretic modeling properties of their points (K. N. Ponomarev);
- Study of the elementary and universal theories of partially commutative groups (Ye. I. Timoshenko);
- The study of Gröbner-Shirshov bases for the various classical groups, algebras and Lie algebras (Ye. N. Poroshenko, A. N. Koryukin , Ye. S. Chibrikov);
- Classification of complete theories with finite number of countable models, in particular the solution to the Lachlan problems; Classification of small theories countable models; a theory of groups polygonometry (S. V. Sudoplatov);
- Classification of countable models of complete theories with continuous number of types (P. V. Sudoplatov, P. A. Popkov);
- The research of the modeling problems of polygons theory (E. V. Ovchinnikova);
- Description of group rings grouped units of finite groups" (A. M. Popova-Ivleva, Ye. V. Grachev);
- Applications of algebra to control theory (A. V. Chekhonadskikh, A. N. Koryukin);
- Research on the job shop scheduling (I. D. Chernykh)
List of the most important scientific projects, developments and other results:
A number of fundamental results of the research into the structure and taxonomy of classical (groups, rings, fields, Lie algebras) and universal algebras, models that have received international recognition. Among them are the theories of varieties skeletons, conditional terms, rigid non-associative algebras and rings, partially commutative groups. Lachlan problem of the countable models of stable theories has been solved.
The research group staff have developed methods for the classification of complete theories countable models, methods for the classification of the universal algebras and functional clones according to their derived structures, the algorithms for the group units of group rings description, approaches to the Groebner bases calculation of non-associative algebras, methods of algebra application in control theory.
Over 500 papers have been published in leading scientific journals, such as: "Algebra and Logic", Siberian Mathematical Journal", "Fundamental and Applied Mathematics", "Russian Mathematical Surveys", "Journal of Symbolic Logic" , "Algebra Universalis" , "Periodica Mathematica Hungary" , "International Journal of Algebra and Computation" , "Communications in Algebra" and others.
Textbooks of S. V. Sudoplatov, and Ye. V. Ovchinnikova "Discrete Mathematics" and "Mathematical Logic and Theory of Algorithms", as a part of textbooks complex on mathematical logic written by a large team of authors from Siberian Branch of Russian Academy of Sciences was awarded the 2010 Russian Government Prize in the field of education for the cycle of works "Concept of Logic and Mathematics Education Forming at the Higher School"
Founders and heads:
Pinus Alexander Georgievich
Doctor of Physical and Mathematical Sciences,
Professor, Corresponding Member of International Higher Education Academy of Sciences,
Honored Worker of Higher School
Ponomarev Konstantin Nikolaevitch
Doctor of Physical and Mathematical Sciences,
Professor
