Helmut Hofer

Institute for Advanced Study, Princeton

Day 1 (April 19) @ 10:10 – 11:10 Keynote

Title: A Short History of Symplectic Dynamics

Although it is difficult to give a precise definition of the emerging field of Symplectic Dynamics, it is not difficult to give examples demonstrating how ideas from Dynamical Systems and Symplectic Geometry/Topology come together to answer nontrivial questions. The modern theory of Dynamical Systems and the field of Symplectic Geometry emerged from Poincaré’s integrated viewpoint of Mathematics. He combined ideas from Geometry, Topology and Dynamical Systems to study Hamiltonian Dynamics. After Poincaré, the theory of Dynamical Systems and Symplectic Geometry developed almost independently, and the latter even gave birth to the new field of Symplectic Topology. In the last twenty years we have seen breakthroughs on a variety of dynamical system problems using integrated ideas, which result from the merger of viewpoints coming from the different fields. These developments point to a new fruitful direction of research, which we call Symplectic Dynamics. In this talk for a general mathematical audience we shall describe some of the ideas and how they came about.