The subleading asymptotics of the ECH spectrum

Abstract: Embedded contact homology can be used to associate a sequence of spectral invariants, called ECH spectral invariants, to any closed three-manifold with a contact form. In previous joint work, we proved a “Volume Property” that recovers the volume of any such manifold from the asymptotics of its ECH spectral invariants. I will discuss recent work aimed at better understanding the subleading asymptotics of this sequence. The main subject of my talk will be a joint work with Nikhil Savale in which we prove a new bound on the growth rate of the subleading asymptotics. I will also briefly mention a conjecture, due to Hutchings, concerning recovering the “contact Ruelle invariant” from the subleading asymptotics.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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