4 problems

Let $X$ be the symplectic four-manifold under consideration, let $\mathcal P:{\mathcal L}(X)\to {\rm Sh}_{H}^+(X)$ be the projection assigning to a Lagrangian torus its area class,…

Folklore conjecture. Every non-monotone Lagrangian torus in $\mathbb{R}^4$ is Hamiltonian isotopic to a product torus.

Let $\mathbb{R}^4$ be equipped with its standard symplectic structure, and consider Lagrangian tori in it up to Hamiltonian isotopy. Product tori and Chekanov tori are two known ty…

Let $(W;L_0,L_1)$ be an exact Lagrangian cobordism, and let a Lagrangian suspension denote the suspension associated to a Hamiltonian isotopy. Biran and Cornea's conjecture. Any ex…