9 problems

Let $(M,\omega)$ be a closed integral symplectic manifold, meaning that $[\omega]/\pi$ is an integral cohomology class, and let $c_G(M,\omega)$ denote its Gromov width. Biran's con…

Let $n\geq 1$ and let $\omega$ be a symplectic form on $S^2\times\mathbb R^{2n}$. Write $c_G(\omega)$ for the Gromov width of $(S^2\times\mathbb R^{2n},\omega)$, and let…

Small-sets nonbarrier conjecture. The Gromov width of $B^{2n}_1\setminus A$ equals $\pi$.

Let $K$ be a compact Lie group, let $\mathcal{O}_{\lambda}$ be the coadjoint orbit through a point $\lambda$ in a positive Weyl chamber, and equip it with its Kostant--Kirillov--So…

Let $(M,\omega)$ be an integral symplectic manifold, meaning that its symplectic form represents an integral cohomology class. The Biran conjecture. All obstructions to symplectic…

Let $K$ be a compact Lie group, let $\mathfrak k^*$ be the dual of its Lie algebra, and let $(\mathcal{O}_{\lambda},\omega^{KKS})$ be the coadjoint orbit through a point $\lambda$…

Let $(M,\omega)$ be a symplectic manifold and consider symplectic embeddings of standard balls into $M$. An obstruction to such an embedding is a condition preventing the embedding…

Let $G$ be a compact connected simple Lie group, let $\lambda\in\operatorname{Lie}(G)^*$, and let $\mathcal{O}_\lambda$ be the coadjoint orbit through $\lambda$, equipped with its…

Gromov-width conjecture. The Gromov width of $\mathcal{M}(r)$ is