# On the Gromov width of polygon spaces

-
Alessia Mandini , University of Pavia
Fine Hall 322

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 tecniques 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. This is joint work with Milena Pabiniak, IST Lisbon.