8 problems

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…

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

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

Let $\underline{L}$ be a pre-monotone Lagrangian link in the disc, and let $\norm{\cdot}_{\underline{L}}$ denote its Hofer pseudonorm on the associated braid group. Metric conjectu…

Let $(M,\omega)$ be a closed and connected symplectic manifold, and let $\operatorname{Ham}(M,\omega)$ be its group of Hamiltonian diffeomorphisms equipped with Hofer's metric…

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 closed symplectic manifold. Write $Ham(M,\omega)$ for the group of Hamiltonian diffeomorphisms, and let $e$ be the norm on $Symp(M,\omega)_0$ defined by sympl…