Seidel's generation conjecture for symplectic mapping classes of rational surfaces

Let $X= \mathbb{CP}^2\#k\overline{\mathbb{CP}}^2$. Write $\pi_0\operatorname{Symp}(X)$ for the group of symplectic mapping classes, and call a symplectomorphism a Lagrangian Dehn twist when it is the Dehn twist associated to a Lagrangian sphere in $X$. Seidel's generation conjecture. $\pi_0\operatorname{Symp}(X)$ is generated by Lagrangian Dehn twists. This conjecture concerns the structure of symplectic mapping class groups and their relation to monodromies from algebraic geometry. It is known for $k\leq 4$, while the cases with larger $k$ remain largely unresolved.