  Via considerations of symplectic reduction, monodromy, mirror symmetry and
Chern-Simons functionals, a conjecture is proposed on the existence of special
Lagrangians in the hamiltonian deformation class of a given Lagrangian
submanifold of a Calabi-Yau manifold. It involves a stability condition for
graded Lagrangians, and can be proved for the simple case of $T^2$.
