8 problems

Let $\mu=(m_1,\ldots,m_n)$ be a partition of $2g-2$, and let $\mathbb P\mathcal H(\mu)$ be a varying stratum of holomorphic differentials up to scaling. Let … where…

Let ${\cal M}^{\cal H}_{(2g-2)}$ and ${\cal M}^{\cal H}_{(g-1,g-1)}$ denote the hyperelliptic components of the corresponding moduli spaces of holomorphic differentials, and let…

Let ${\cal M}_{\bf d}$ be a moduli space of holomorphic 1-forms with prescribed zero orders, and let ${\cal M}$ be one of its connected components. A group is commensurable with an…

Let $\mathcal H(\mu)$ be a stratum of holomorphic differentials, and let $\pi_1^{\rm orb}(\mathcal H(\mu))$ denote its orbifold fundamental group. The orbifold universal cover of…

Let $a$ be fixed, and suppose that $r$ is even and $a$ is odd. Let $W_g^\pm(a,r)$ denote the refinement of Witten's class according to spin parity, and let…

The multiplicities $m_i-2$ are determined by the singularity $(C,p)$ via its conductor, and hence determine a stratum of holomorphic differentials. Connected-component conjecture.…

Labourie's conjecture. The map $\Psi$ is a diffeomorphism. This conjecture concerns a canonical parametrization of the Hitchin component by a Riemann surface together with higher h…

Let $\Sigma$ be a surface, and let $\mathcal{A}(\lambda)$ be a family of $\operatorname{PSL}_n(\mathbb{C})$-connections satisfying … with…