The workshop is on geometric methods in dynamics. We want to explain how simple geometric ideas can be used to obtain deep results in dynamics, such as the precise count of geodesics on surfaces of negative curvature, the count of periodic orbits of Hamiltonian systems on tori, and the existence of periodic orbits of a prescribed energy of classical mechanical systems.
It is usual that students learn elements of dynamical systems, often with a focus to applications, and that they also learn some Riemannian geometry. In particular, in Chile, and the countries around it, there is a tradition in low-dimensional dynamical systems. Modern dynamical systems and geometry benefit from the close interac-tions between the two theories, and in particular geometry helps to understand global aspects of dynamical systems. Our main goal is to bring out some of these connections in elementary and beautiful examples.
We hope that from teaching geometry and dynamics by examples and by stressing their interactions, the students will not only better understand parts of both theories, but also see how beautifully different mathematical theories interact and enrich each other.
Most of the talks will be given in Spanish. Sheila Sandon, David Frenkel and Felix Schlenk will lecture in French or English, according to the students preference.
The students should have a working knowledge in real analysis of several variables and on curves and surfaces. More knowledge is useful, but not necessary to follow the lectures.