Spectral invariants defined via Embedded Contact Homology (ECH) or the closely related Periodic Floer Homology (PFH) satisfy a Weyl law: Asymptotically, they recover symplectic volume. This Weyl law has led to striking applications in dynamics (smooth closing lemma) and symplectic geometry (simplicity conjecture). In this talk, I will report on work in progress concerning the subleading asymptotics of symplectic Weyl laws. I will explain the connection to symplectic packing problems and the algebraic structure of groups of Hamiltonian diffeomorphisms and homeomorphisms.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
