Algebraic, differential, geometric and topological structures and their exploitation in theoretical and applied fields
| Programmee: | Institutional Projects |
| Code: | 011303 |
| Execution period: | 2024 – 2027 |
| Institutions: | Vladimir Andrunachievici Institute of Mathematics and Computer Science, Moldova State University |
| Project Leader: | Damian Florin |
| Participants: | Algebra and Topology, Differential Equations |
Summary
The subprogram is focused on the research of some current problems in mathematics. Among its objectives we will mention the application of modern and global methods (analytical, algebraic, geometric, and topological) in the in-depth study of equations and systems of differential equations, studying the behavior of solutions of nonlinear singularly perturbed systems governed by differential, integro-differential operators, studying asymptotic properties in dynamic systems; studying the solvability of singular integral equations in functional spaces, etc.. Another objective related to the field of algebra is the development of the theory of quasigroups and non-associative systems with different identities, including properties necessary for planning experiments, applying codes and encrypting information, applying lattice methods in the study categorie of module, rings and group topologies, in the study of the interconnections between the algebraic-topological properties of groups and rings with their automorphism groups and their continuous endomorphism rings, equipped with different topologies, the study of the geometry of hyperbolic manifolds.
The subprogram represents a continuation of the research carried out by the authors within national and international projects. Its realization will allow the theoretical development of some important fields of mathematics, the unification of research on adjacent fields, as well as the finding of new ways of applying them. The subject matter included in the project is important both from the point of view of the further development of the theory of differential equations and dynamic systems, as well as their applications. Both modern research methods and methods developed in mathematics schools in Moldova will be used. We will mention the methods: qualitative theory of systems of differential equations; algebras and Lie groups, methods of the theory of algebraic invariants of polynomial systems of ordinary differential equations; theory of stability according to Lyapunov, abstract algebra, isotopic transformations of quasigroups, discrete geometry on hyperbolic manifolds, theory of holomorphic functions of several complex variables. The subprogram foresees obtaining new results, both theoretical and applied.
