Orderability, contact non-squeezing, and Rabinowitz Floer homology

In 2000 Eliashberg-Polterovich introduced the natural notion of orderability of contact manifolds. This is closely related, as discovered by Eliashberg-Kim-Polterovich, to (non-)squeezing in contact geometry. I will explain how one can study orderability questions using the machinery of Rabinowitz Floer homology: in particular how non-vanishing of Rabinowitz Floer homology implies orderability and new non-squeezing results. I will establish a link between orderable and hypertight contact manifolds, and show that the Weinstein Conjecture holds (i.e. there exists a closed Reeb orbit) whenever there exists a positive (not necessarily contractible) loop of contactomorphisms.