UC Berkeley

This dissertation is a collection of four papers involving embedded contact homology (ECH). ECH is a three-manifold invariant recently defined by Michael Hutchings. The dissertation covers both technical results about ECH (for example a proof that the absolute grading in ECH is a topological invariant) and applications of ECH to Reeb dynamics and symplectic embedding problems. All four papers were written while the author was a graduate student at UC Berkeley.