Appears in collection : Summer School 2015: Moduli Problems in Symplectic Geometry

Special Lagrangians in Calabi-Yau manifolds are expected to be plentiful. However, in practice, it is difficult to find special Lagrangian submanifolds in compact Calabi-Yau manifolds except for two special classes: fixed points of anti-symplectic involutions and holomorphic Lagrangians in hyper-Kahler manifolds. Thus it is natural to look for a modified special Lagrangian condition that reduces to the standard one in those two cases. I will describe how moduli spaces of holomorphic disks give rise to such a modification of the special Lagrangian condition. This is joint work with G. Tian