C^0 Limits of Hamiltonian Paths and Spectral Invariants

After reviewing spectral invariants, I will write down an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C⁰-distance of its flow from the identity. I will also show that, unlike the Hofer norm, the spectral norm is C⁰-continuous on surfaces. Time permitting, I will present an application to the study of area preserving disk maps.