McDuff and Schlenk introduced the embedding capacity function of a 4-ball, which describes when a four-dimensional ellipsoid fits inside a four-dimensional ball in a manner that preserves the symplectic form. In this talk, we will describe embedding capacity functions for toric targets and discuss how momentum-map-like pictures can shed light on computing this function.

We will focus on specific examples and give a broad overview of the recent results in this area.