Symplectic embedding, systolic inequalities and celestial mechanics

The goal of this school is to explain several methods and result from modern Riemannian and symplectic geometry and from Hamiltonian systems, and to use them to study old problems in celestial mechanics. Among the tools are symplectic embeddings by elementary and less elementary methods, J-holomorphic curves, and systolic inequalities in Riemannien, contact and symplectic geometry. We shall apply these tools to study very explicit problems on the motion of Moon, Earth, and Sun in the form of the restricted 3-body problem and several of its limits.

This will show that the modern methods we use are by no means dry mathematical abstractions, but have their origin in concrete problems in mechanics, geometrical optics, and celestial mechanics.

Prerequisites: We expect that students have had courses in real analysis of several variables, know what an ordinary differential equation is, and have followed a course on curves and surfaces. More knowledge is useful,  but not necessary to follow the lectures.