Subleading Asymptotics of ECH Capacities and Symplectic Packing Problems

We compute the subleading asymptotics of the ECH and elementary ECH capacities of toric domains and show that they recover the perimeter in the liminf, without any genericity required.  As an application, we give the first examples of the failure of packing stability for compact manifolds with smooth boundary or with no boundary at all, addressing a question of Schlenk.  There are implications for long-term super-recurrence and ellipsoid embedding functions and if time allows I will also discuss a connection with symplectic tiling.   This will report on joint works with Hind, Magill, and McDuff.