Umberto Leone Hryniewicz (RWTH Aachen University)
We prove that every Reeb flow on a closed connected three-manifold has either two or infinitely many periodic orbits, if the first Chern class of the associated contact structure is torsion. This result covers Reeb flows on the three-sphere, and implies that every Finsler metric on a closed surface has either two or infinitely many closed geodesics. Joint work with Cristofaro-Gardiner, Hutchings and Liu.