(いつもと曜日が違います.ご注意ください)
Holomorphic curves are a very useful tool for studying the topology and dynamics of symplectic manifolds. I will start with an overview of how holomorphic curves can detect periodic orbits of symplectic diffeomorphisms, taking the viewpoint pioneered by Hofer in 1993. Then, I will discuss a new method using “low-action” holomorphic curves to detect closed invariant subsets that might be more general than periodic orbits. This has a few applications. I will mention one of them: a generalization to higher genus surfaces of a theorem by Le Calvez and Yoccoz. Time permitting, I will mention some of the other applications. The talk is based on joint work with Dan Cristofaro-Gardiner, and will not assume any prior knowledge of holomorphic curves.