Abstract: 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 is non-trivial: there are manifolds with infinite volume but finite Gromov width.

Gromov widths and solutions of associated symplectic packing problems (how many disjoint balls of given area can one embed symplectically into a given manifold) 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 various techniques for studying the Gromov width of symplectic manifolds with a focus on Hamiltonian spaces. Time permitting I will conclude by discussing lower bounds for the Gromov width of multiplicity-free spaces, which is current work in progress.