5 problems

Let $S$ be a compact complex surface in the Kodaira class ${\rm VII}$. Write ${\mathcal T}(S)$ for its set of Lee classes, viewed in $H^1_{dR}(S,\mathbb R)$ and ordered along…

Let $M$ be a closed manifold of dimension at least $4$, and let $\omega=d^{\alpha}\lambda$ be an exact locally conformally symplectic form on $M$ whose Lee form $\alpha$ is rationa…

Let $M$ be a closed manifold of dimension at least $4$, and let $(\lambda,\alpha)$ be an exact locally conformally symplectic structure, with $\alpha$ a rational Lee form. Define t…

Let $(M,\lambda,\alpha)$ be an exact locally conformally symplectic structure, meaning that $\alpha$ is a closed $1$-form and $\omega=d^{\alpha}\lambda$ is non-degenerate. Define t…

Holomorphic Seifert–Weinstein conjecture. For any l.c.s. pair $(\omega,J)$ on $S^{2k+1}\times S^1$ or on $C\times S^1$ for $C$ a threefold, there is an elliptic, non-constant $J$-h…