  We show that, up to Lagrangian isotopy, there is a unique Lagrangian torus
inside each of the following uniruled symplectic four-manifolds: the symplectic
vector space $\mathbb{R}^4$, the projective plane $\mathbb{C}P^2$, and the
monotone $S^2 \times S^2$. The result is proven by studying pseudoholomorphic
foliations while performing the splitting construction from symplectic field
theory along the Lagrangian torus. A number of other related results are also
shown. Notably, the nearby Lagrangian conjecture is established for
$T^*\mathbb{T}^2$, i.e.~it is shown that every closed exact Lagrangian
submanifold in this cotangent bundle is Hamiltonian isotopic to the
zero-section.
