The C^0-flux conjecture for Hamiltonian diffeomorphisms

Let $(M,\omega)$ be a closed connected symplectic manifold. Denote by $\operatorname{Symp}(M,\omega)$ the group of symplectomorphisms, by $\operatorname{Symp}_0(M,\omega)$ its identity component, and by $\operatorname{Ham}(M,\omega)$ the group of Hamiltonian diffeomorphisms. C$^0$-flux conjecture. The subgroup $\operatorname{Ham}(M,\omega)$ is $C^0$-closed in $\operatorname{Symp}_0(M,\omega)$. This conjecture concerns the $C^0$-topological rigidity of Hamiltonian diffeomorphisms and is associated with the theorem of Gromov and Eliashberg on smooth elements of the $C^0$-closure of the symplectomorphism group. Its resolution is not specified in the source.