Arnol'd's Lagrangian intersection conjecture

Let $L$ be a closed smooth manifold and let $T^*L$ denote its cotangent bundle. For every compactly supported Hamiltonian diffeomorphism $\phi$ of $T^*L$, consider the intersection points of the zero section $L$ with its image $\phi(L)$. Arnol'd's conjecture. The number of intersection points $\phi(L)\cap L$ is bounded from below by the minimal number of critical points of a smooth function on $L$. This is the Lagrangian version of Arnol'd's conjecture for cotangent bundles and motivates lower bounds for Lagrangian intersections; the source does not provide enough information here to determine whether the conjecture has been resolved.