9 problems

Extension conjecture. For all symplectic manifolds $(M,\omega)$ such that

Bounded isometry conjecture. For all $(M,\omega)$,

El Hadrami's conjecture. The subgroup $\widetilde{\mathcal T}$ behaves like the maximal torus $\mathcal T$ in $\operatorname{Diff}_\omega(A)=\operatorname{Symp}_\omega(A)$ and can…

Let $\mathcal{X}$ be an unbounded metric space. Call $\mathcal{X}$ large if its asymptotic space in some (or every) nonstandard model $M$ contains a subspace isometric to…

Stability conjecture. The reduced symplectic cone should admit a chamber partition such that the homotopy type of the symplectomorphism group is invariant within each chamber.

Let $M_g=Sigma_g\times S^2$ be a topologically trivial ruled surface, and let $M_g\#\overline{n\mathbb{C}P^2}$ denote its $n$-point blow-up. Write a normalized symplectic form as…

Special-case subalgebra conjecture. In all special cases, the homotopy Lie algebra of $G_{c_1,c_2,c_3}$ is a subalgebra of the homotopy Lie algebra for the generic case.

Let $(M,\omega)$ be a symplectic manifold, let $\operatorname{Symp}_0(M,\omega)$ be its identity component, and let $\operatorname{Ham}(M,\omega)$ be the Hamiltonian subgroup. Let…

Let $(M,\omega)$ be a closed symplectic manifold such that $\operatorname{Symp}_0(M,\omega)$ is not identical to $\operatorname{Ham}(M,\omega)$. The spectral metric extension conje…