The Spectral Diameter of a Liouville Domains and its Applications

The spectral norm provides a lower bound to the Hofer norm. It is thus natural to ask whether the diameter of the spectral norm is finite or not. During this short talk, I will give a sketch of the proof that, in the case of Liouville domains, the spectral diameter is finite if and only if the symplectic cohomology of the underlying manifold vanishes. With that relationship in hand, we will explore applications to symplecticaly aspherical symplectic manifolds and Hofer geometry.