
Symplectic Geometry Seminar
Spectral Capacity of Symplectic Ellipsoids
The spectral norm on the group of Hamiltonian diffeomorphisms of a symplectic manifold is defined via a homological min-max process on the filtered Floer homology. Based on the spectral norm one defines the spectral capacity of domains which is closely related to the Hofer-Zehnder capacity and the displacement energy capacity, in particular it is long known that it is bounded by twice of the latter. In this talk, we compute the exact value of the spectral capacity of balls in $\mathbb{C}^{n}$ which upgrades the displacement energy bound by a factor of two. As a corollary, we calculate spectral capacity of symplectic ellipsoids and polydisks and also recover the two-ball packing theorem of Gromov. We will also compute the spectral capacity of some balls in projective spaces. This is joint work with M.S. Atallah and D. Cant.