Michael Hutchings of the Institute for Advanced Study gives a Special Members' Colloquium on Reeb vector fields, the dynamical systems that arise naturally on odd-dimensional contact manifolds. He opens with the basic setup before narrowing to three dimensions, where Seiberg-Witten theory gives far sharper results than are available in higher dimensions. The centerpiece is Irie's closing lemma, which shows that a periodic orbit can always be created through any given region by an arbitrarily small smooth perturbation of the vector field. Hutchings presents his own quantitative refinement of that result, pinning down roughly how small a perturbation is needed to produce an orbit of a given period: a perturbation of size on the order of 1/L suffices to create an orbit of period at most L. The talk is pitched as an introduction for a broader special year on vector field dynamics, so it builds up the geometric and topological context rather than assuming prior familiarity with contact geometry or Seiberg-Witten invariants.