On the Gromov width of polygon spaces

After Gromov's foundational work 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 \((r_1,\ldots, r_n)\). 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.