Northern California Symplectic Geometry Seminar: Subleading asymptotics of ECH capacities

Seminar | April 1 | 4-5 p.m. | 740 Evans Hall

 Dan Cristofaro-Gardiner, UC Santa Cruz

 Department of Mathematics

In previous work, Hutchings, Ramos and I studied the embedded contact homology (ECH) spectrum for any closed three-manifold with a contact form, and proved a “volume identity” showing that the leading order asymptotics recover the contact volume. I will explain recent joint work that sharpens this asymptotic formula by estimating the subleading term. The main technical point needed in our work is an improvement of a key spectral flow bound in Taubes' proof of the three-dimensional Weinstein conjecture; the main goal of my talk will be to explain the ideas that go into this improvement. I will also discuss some possibilities for obtaining sharp asymptotics.