Mathematical Conversations

Embedded Contact Homology (ECH) is a Floer type invariant due to Hutchings. This talk provides a gentle overview of ECH (in part through a video of the Hopf fibration) and sketches why ECH of a prequantization bundle over a Riemann surface is isomorphic as a $Z/2Z$-graded group of the exterior algebra of its base, a result from the 2011 PhD thesis of Farris. We explain an extension of this result in joint work with M. Weiler. We also comment on future work relating to ECH of Seifert fiber spaces with applications to surface dynamics.