8 problems

Let $M$ be a symplectic manifold that admits a toric structure. An almost toric fibration of $M$ may contain nodal fibers obtained by nodal trades, while a toric fibration has only…

Let $(M,\omega)$ be a symplectic four-manifold containing a top-dimensional submanifold with boundary that is diffeomorphic to an almost toric manifold whose base has a one-stratum…

Let $M$ be a rigid del Pezzo surface. An index zero $(p,q)$-unicuspidal rational symplectic curve in $M$ is as in the source, and an almost toric fibration is a fibration…

Let $(M,\omega)$ be a symplectic $4$-manifold. A toric fibration is a toric Lagrangian fibration on $(M,\omega)$, and a path of almost toric fibrations is a continuous family of al…

Let $(X,c\omega)$ be a symplectic $4$-manifold. An almost toric fibration is a Lagrangian fibration with only nodal and elliptic singularities. Let $\mathcal{ATF}(X,\omega)$ denote…

Almost-toric-fibre isotopy conjecture. Any Lagrangian torus in $\mathbb{C}P^2$ is isotopic to some $(a,b,c)$-ATF fibre.

Let two monotone Lagrangian fibers of almost toric fibrations lie in the same symplectic manifold, and suppose their almost toric base diagrams have different orbifold limits. The…

Let $M$ be a symplectic manifold with an almost toric fibration (ATF), and let an almost toric base diagram (ATBD) describe it. Assume the cuts of the ATBD lie inside the eigenline…