Equivariant symplectic capacities

We define a sequence of symplectic capacities using positive S^1-equivariant symplectic homology. These capacities are conjecturally equal to the Ekeland-Hofer capacities. However they satisfy axioms which allow them to be computed for many examples, such as convex toric domains. They also give sharp obstructions to symplectic embeddings of cubes into convex toric domains. The asymptotics of these capacities are conjecturally related to Lagrangian embeddings. This is a joint work with Jean Gutt.