The study of Hamiltonian dynamical systems plays a fundamental role in many different contexts, both in pure and applied mathematics. Indeed, most of the physical laws ruling our everyday lives --the motion of the celestial bodies in the universe, the geodesic flow on a manifold, a large set of mechanical systems-- they all share a common feature consisting in what is called a ''Hamiltonian structure''.
Recent advances in the study of Hamiltonian systems have been made possible thanks to a fruitful interaction between diverse ideas and techniques coming from dynamical systems, nonlinear analysis, PDE theory and symplectic geometry.
The School-Workshop aims at outlining these interactions and consist of 4 courses (6 hours each) lectured by well-known experts in the field.