After Gromov’s foundational work in in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold $(M,\omega)$ is a symplectic invariant that measures, roughly speaking, the size of the biggest ball we can symplectically embed in $(M,\omega)$.

I will discuss techniques to compute the Gromov width of a special family of symplectic manifolds, the moduli spaces of polygons in $\mathbb{R}^3$ with edges of lengths $(r_1, ..., r_n )$. Under some genericity assumptions on lengths $r_i$, the polygon space is a symplectic manifold. After introducing this family of manifolds, I will concentrate on the spaces of $5$-gons and calculate their Gromov width. I will also discuss higher dimensional polygon spaces, in particular the $6$-gons case.

This is joint work with Milena Pabiniak, IST Lisbon.