Mirzakhani's conjecture on higher-rank affine invariant submanifolds

Let $\mathcal{N}$ be a higher-rank affine invariant submanifold of a stratum of translation surfaces. A translation surface is not primitive if it covers a quadratic differential of lower genus. Mirzakhani's conjecture. Every higher-rank affine invariant submanifold $\mathcal{N}$ is either a stratum or is not primitive, in the sense that every translation surface in it covers a quadratic differential of lower genus. In the non-primitive case, $\mathcal{N}$ should arise from a covering construction, but it remains open to determine exactly which such constructions are possible.