5 problems

Let ${\mathcal C}$ be an affine invariant manifold of rank $\ell\geq 2$, and let a rank $\ell$ submanifold be given inside ${\mathcal C}$. A flexible vector field for…

Let $\mathcal{M}$ be an affine manifold in a stratum of translation surfaces. Its rank is the dimension of its tangent space projected to absolute cohomology divided by $2$, and…

Let ${\mathcal C}$ be an affine invariant manifold of rank $\ell\geq 1$. An affine invariant manifold is a submanifold of a stratum of abelian differentials locally defined by homo…

Mirzakhani's conjecture. If an affine invariant submanifold $\cM$ is not defined over $\bQ$, then $p(T(\cM))$ has dimension $2$.

Mirzakhani's conjecture. If an affine invariant submanifold $\cM$ is defined over $\bQ$, and $\cM$ is not a connected component of a stratum, then every translation surface in…