Workshop on Recent Developments in Symplectic Dynamics

Hofer, Wysocki and Zehnder conjectured in the year 2000 that every Reeb flow on the standard contact three-sphere admits either exactly two or infinitely many periodic orbits. This conjecture was settled as a result of joint work with Cristofaro-Gardiner, Hutchings and Liu.
The main theme of this talk is quantitative refinements of this conjecture. Emphasis will be given to a refinement of an ergodic nature, and to one concerning growth rates of periodic orbits. In particular, we will mention the work of Albach (who recently graduated in Aachen) where it is proved that for every reversible Finsler metric on the two-sphere the following holds: the growth of closed geodesics with respect to period is at least quadratic. This largely improves previously known growth rates due to Hingston.