Abstract

Born from the principle of conservation of energy at the beginning of the 19th century, Hamiltonian mechanics still gives a successful description of conservative systems in contemporary physics. In recent years, Hamiltonian mechanics has also brought mathematicians to the study of a new type of geometry characterized by many unexpected features and intriguing open questions. In this talk we will focus on current research themes in this so-called symplectic geometry which are connected to seemingly unrelated topics such as the uncertainty principle, Fibonacci numbers and the volume of convex bodies.