Topology Seminar: Sub-leading asymptotics of ECH capacities

Seminar | October 16 | 4:10-5 p.m. | 3 Evans Hall

 Nikhil Savale, Universität zu Köln

 Department of Mathematics

On a closed, contact three manifold the asymptotics of its ECH spectrum are known to recover the contact volume. This has applications to the existence of at least two, and in some cases two or infinitely many, Reeb orbits as well as the density of the union of periodic Reeb orbits for generic contact forms. In this talk, we improve the asymptotic formula for ECH spectrum with a subleading estimate. This has applications to a Weyl law for the ECH spectrum and the region of analyticity of the ECH zeta function.