Geometry, Mechanics, and Control - Young Researchers Workshop

Explore advanced topics in differential geometry, optimal control theory, and mathematical physics through this comprehensive workshop featuring leading researchers in the field. Delve into the Pontryagin maximum principle across three detailed sessions, examining its applications in optimal control problems. Investigate topological equivalence in linear quadratic optimal control and discover how local symmetries reduce complexity in field theories. Study the stratification of transverse momentum maps and learn about evolution vector fields on contact manifolds with applications to thermodynamics. Master infinite-dimensional geometry through a three-part series covering both theoretical foundations and practical applications. Examine stochastic processes on surfaces within 3-dimensional contact sub-Riemannian manifolds and explore covariant brackets in particle dynamics and first-order Hamiltonian field theories. Understand geometrical splitting methods for contact Hamiltonian systems and analyze the dynamics of two charged particles on spherical surfaces. Conclude with an exploration of the topology of Bott integrable fluids, connecting geometric structures to fluid dynamics.