# On the Gromov width of polygon spaces

 Princeton/IAS Symplectic Geometry Seminar Topic: On the Gromov width of polygon spaces Speaker: Alessia Mandini Affiliation: University of Pavia Date: Friday, October 31 Time/Room: 1:30pm - 2:30pm/S-101 Video Link: http://video.ias.edu/pisgs/2014/1031-AlessiaMandini

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.