Holomorphic curves in low-dimensional dynamics
Abstract. The talk surveys some of the recent developments concerned with the use of holomorphic curves in the study of low-dimensional Hamiltonian systems. For example holomorphic curves can be used to construct global surfaces of section (or generalizations thereof) with quite minimal knowledge about the global dynamics. A complete picture can be obtained for large classes of Reeb flows on the three-sphere. The talk also surveys some of the open questions concerning the extension of the theory to autonomous Hamiltonian flows on three-dimensional energy surfaces of contact-type.