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12 - 16 February 2018, Department of Mathematics “Tullio Levi-Civita”, University of Padova

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 topology.

The School aims at outlining these interactions, and consist of four courses (6 hours each) lectured by well-known experts in the field.

M.-C. Arnaud (UAPV) Tonelli Hamiltonians and their integrability.

G. Benedetti (Uni Leipzig) Systolic inequalities in contact and symplectic geometry.

A. Fathi (Georgia Tech) T.B.A.

V. Humilière (IMJ-PRG) Action selectors from symplectic topology and applications.

Speakers will outline a panorama of the state of the art, with emphasis on their recent contributions to the field. The School is aimed at PhD and all researchers interested in Hamiltonian dynamical systems and related topics. Contributed talks concerning the themes of the School are welcome and will be selected by the Committee.