4 problems

Let $(W,\omega)$ be a closed symplectic manifold with integral symplectic class, and let $W_0$ be an embedded symplectic hypersurface representing the homology class dual to…

Atiyah–Seidel conjecture. Non-uniruled symplectic manifolds admit no Hamiltonian torsion; equivalently, the Hamiltonian diffeomorphism group contains no nontrivial finite-order ele…

A polarisation of a symplectic manifold $(M,\omega)$ is a pair $(M,\Sigma)$ where $\Sigma\subset M$ is a symplectic hypersurface, and its degree is the number $d\in\mathbb{N}$ asso…

Hard Lefschetz failure conjecture. Most $X_{k,\tau}$ with even first Betti number do not satisfy the Hard Lefschetz Theorem.