Abstract: Singular symplectic spaces appear naturally as examples of
reduced Hamiltonian phase spaces in physics as well as singular projective
algebraic varieties in mathematics. We give a unified and geometric
definition for these objects, and prove a singular variant of the
Gromov-Tischler theorem: such a space with an integral symplectic form can
always be embedded symplectically inside the complex projective space. On
the way we discuss the topology of stratified spaces, symplectic reduction
and h-principles. This is joint work with Mahan Mj.