Pseudoholomorphic curves in symplectic geometry

Abstract:

Pseudoholomorphic curves were introduced by Gromov as a fundamental tool for the study of symplectic manifolds. I will review some applications of pseudoholomorphic curves in symplectic geometry, which often crucially rely (among other things) on a version of Gromov's compactness result for pseudoholomorphic curves. Then I will discuss some basic facts at the core of Gromov's compactness result, with the goal of conveying why and in what settings such a result can be expected.