6 problems

Let $n<9$, and consider the rational surface $\mathbb{CP}^2 \# n\,\overline{\mathbb{CP}}{}^2$. A symplectic torus is an embedded symplectic surface of genus one, and two such tori…

Let $E$ be a relatively minimal sphere bundle over a sphere, equipped with a complex structure, and let $S\subset E$ be a connected symplectic submanifold. Siebert–Tian symplectic…

Local completeness conjecture. These canonical smoothings, including the curves obtained by smoothing arbitrary subsets of the nodes of $C_{\mathrm{nod}}$, comprise all possible sy…

Let $C\subseteq \mathbb{CP}^2$ be a smooth or nodal symplectic curve. Symplectic isotopy conjecture. Every such curve $C$ is symplectically isotopic to a projective algebraic curve…

Let $M_g=\Sigma_g\times S^2$ be a minimal topologically trivial ruled surface equipped with a symplectic form $\omega$. A symplectomorphism of $(M_g,\omega)$ is symplectically isot…

Let $S$ be a smooth symplectic surface in $\mathbb{C}\textup{P}^2$. Two such surfaces are symplectically isotopic if they are connected by an isotopy through smooth symplectic surf…