We fix an arbitrary symplectic toric manifold M. Its real toric lagrangians are the lagrangian submanifolds of M whose intersection with each torus orbit is clean and an orbit of the subgroup of elements that square to the identity of the torus (basically that subgroup is $\{ 1 , -1\}^n$). In particular, real toric lagrangians are transverse to the principal torus orbits and retain as much symmetry as possible.

This talk will explain why any two real toric lagrangians in M are related by an equivariant symplectomorphism and, therefore, any real toric lagrangian must be the real locus for a real structure preserving the moment map. This is joint work with Yael Karshon.