Creating Periodic Orbits of Reeb Vector Fields in Three Dimensions

Michael Hutchings introduces Reeb vector fields and explains why their periodic orbits are substantially better understood in three dimensions through Seiberg-Witten theory. The colloquium develops Irie's closing lemma, which creates a periodic orbit through a selected region after a small perturbation, and discusses a quantitative refinement connecting the perturbation size to an upper bound on the orbit period.