Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems

This project is envisioned as a complex, multidisciplinary project in the areas of geometry and topology, with applications both in mathematical physics, and in computational and discrete geometry, and it is meant to ensure a high international level of research quality. The following themes will reserve a special attention. Geometry and dynamics of integrable and closely related systems, especially the ones coming from the classical mechanics and geometry. Extremal problems, varying from general problems of mathematical programming and optimal control to the calculus of variations with applications in mechanics. Problem of matrix pencils completion in the theory of linear systems control. Configuration spaces, including the ones appearing in geometrical and topological combinatorics, such as polygonal configuration spaces occurring in robotics. Problems of embeddings and of mass partitions when the action of the associated symmetry group is not free. The smooth rigid group actions on manifolds. Development of a connection between dynamical systems with integrable and analytical evolution and the number theory, comparative analysis on p-adic, adelic, q-deformed, and noncommutative spaces. Several strategic partnerships will be promoted, such as with SISSA (Italy), the FroM-PDE project of Professor Dubrovin (European Research Council, Investigator Grant Scheme), and Steklov Mathematical Institute, director V. Kozlov, an academician and a vice president of RAS.