The School

«Modern Geometric and Topological Methods
in Problems of Mechanics»

The school is aimed to introduce undergraduate and PhD students to current problems in mechanics (both theoretical and applied) and to help them master modern methods developed in geometry, topology, the theory of dynamical systems, and mathematical physics, which find applications in solving these problems.

Attendees are offered an interconnected series of courses on theoretical mechanics and topological methods applied to integrable and dynamical systems, including geodesic flows and billiards, as well as pseudo-Euclidean analogues of mechanical systems. This "qualitative" approach to their study was organically complemented by geometric constructions that enable the formulation of explicit, exact, and asymptotic solutions to systems in mechanics and physics, including nonlinear waves. Several mini-courses are dedicated to the most recent results obtained by the lecturers and their colleagues.

An important practice-oriented component of the program is a demonstration and laboratory module in robotics, implemented in collaboration with the faculty of the Master's program "Mathematical Robotics and Artificial Intelligence" at Sirius University. One of the mini-courses is focused on the application of neural networks in computer vision.

The school is held with financial support from the Ministry of Science and Higher Education within the program of the Moscow Center for Fundamental and Applied Mathematics under Agreement No. 075-15-2025-345, and with the support of the National Research University Higher School of Economics (HSE) and the Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMech RAS).