4 problems

Let $L$ be a displaceable Lagrangian in a symplectic manifold $M$, and let $d_{C^0}$ be the $C^0$ distance on Hamiltonian diffeomorphisms. Local Hamiltonian nondisplacement conject…

Let $X$ be a closed symplectic manifold. Define … where $d_H$ is Hofer's metric and $\operatorname{Aut}(X)$ denotes the autonomous Hamiltonian diffeomorphisms. Unbounded autonomous…

Let $(M,\omega)$ be a symplectic manifold. For each integer $k\geq 0$, let ${\rm BI}_{k,0}(M)$ be the subgroup of $k$-bounded symplectomorphisms in $\operatorname{Symp}_0(M)$, and…

Let $(M,\omega)$ be a symplectic manifold. Write $\operatorname{Symp}_0(M)$ for the identity component of the symplectomorphism group, and let ${\rm BI}(M)$ be the normal subgroup…