The dynamics of contact manifolds
The dynamics of contact manifolds

Rohil Prasad, Princeton University
Fine Hall 110
An interesting question in dynamics is the following: Does any nonsingular, volumepreserving flow on a threemanifold $M$ necessarily have a periodic orbit?
The answer is unfortunately no in general. However, in the case where $M$ is a contact manifold and the flow is the standard one known as the Reeb flow, the answer turns out to be yes! We’ll discuss an approach to this problem via the study of holomorphic curves in the fourmanifold $\mathbb{R}\times M$.