Gromov width is an invariant of symplectic manifolds that measures the area of the largest ball that can be embedded symplectically. According to Gromov's famous non-squeezing theorem, this invariant captures a non-trivial property of symplectic manifolds: there are manifolds with infinite volume but finite Gromov width.

Gromov widths and solutions of associated symplectic packing problems are generally difficult to obtain. Most results in this direction are either low-dimensional or rely on some form of Hamiltonian symmetry.

In this talk I will describe an idea for bounding the Gromov width of multiplicity-free spaces (a non-abelian generalization of toric manifolds) that builds on techniques recently employed by Pabiniak and others.