Introduction to Symplectic Topology and Hamiltonian Dynamics

Symplectic structures provide the mathematical underpinning for Classical Mechanics. Symplectic Topology is concerned with global questions Hamiltonian dynamics. For example, does a Hamiltonian flow (solution to Hamilton's equations in Classical Mechanics) always have a periodic orbit? Or how many distinct "types of Classical Mechanics" can exist on a given phase space? The field has been revolutionized in the mid 80s through the introduction of pseudo-holomorphic curves by Gromov.

We will explain the terms used and give examples to illustrate these concepts. This talk will serve to provide background for the colloquium talk the following Thursday.