Higher symplectic capacities

We construct a new family of symplectic capacities indexed by certain symmetric polynomials, defined using rational symplectic field theory. We prove various structural properties of the capacities and discuss the connections with the equivariant L-infinity structure on symplectic cohomology and curve counts with tangency conditions. We also give some preliminary computations in basic examples and show that they give new state of the art symplectic embedding obstructions.