3 problems

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The Flux Conjecture
Flux Conjecture. The subgroup $\operatorname{Ham}(M,\omega)$ is $C^1$ close in $\operatorname{Symp}(M,\omega)_0$ ; equivalently, it is $C^1$ -closed there.
Conjecturesolvedflux-conjecture hamiltonian-dynamics symplectic-geometryarXiv posted 2 days ago
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The Lagrangian $C^0$ flux conjecture
Let $(M,\omega)$ be a symplectic manifold, let $L$ be a Lagrangian, and let $\mathcal L_{\mathrm{Ham}}(L)$ be its Hamiltonian orbit inside the space $\mathcal L_{\mathrm{Lag}}(L)$ …
Conjectureopenflux-conjecture lagrangian-submanifolds symplectic-topologyarXiv posted 2 days ago
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The pathwise $C^0$ -Flux conjecture for Hamiltonian isotopies
Pathwise $C^0$ -Flux conjecture. $PHam(M)$ is $C^0$ -closed in $PSymp(M)$ .
Conjectureopenflux-conjecture hamiltonian-isotopies symplectic-topologyarXiv posted 2 days ago

The Flux Conjecture