5 problems

Let $(M,\omega)$ be a symplectic manifold, let ${\rm Diff}_{\rm Ham}(M)$ denote the Hamiltonian diffeomorphism group, and let ${\rm Diff}_{\rm Ham}^k(M)$ be the subspace of diffeom…

Unboundedness conjecture. For every closed symplectic manifold $(M,\omega)$,

Let $(M,\omega)$ be the symplectic manifold under consideration and let $f\in \operatorname{Ham}(M,\omega)$. Define the positive total Hofer norm as the function assigning to each…

Let $(S^2,\omega_{st})$ be the symplectic two-sphere normalized by … Let $inj(M,\omega)$ be the pseudo-injectivity radius, namely the supremum of the radii $r$ such that…

Let $(M,\omega)$ be a closed symplectic manifold, and let $\gamma$ be a Hamiltonian circle action generated by a Morse Hamiltonian. The Hofer index $I^{H}(\gamma)$ is the maximal d…