7 problems

Let $\Sigma_g$ be a closed surface of genus $g\geq 2$. Denote by $\mathcal{B}(\Sigma_g)$ the deformation space of convex $\mathbb{R}\mathbb{P}^2$-structures on $\Sigma_g$, and by…

Polynomial comparability conjecture. The following subsets of $\mathcal{H}(S_{g,m})(\mathbf{L})$ are polynomially comparable to each other:

Polynomial growth conjecture. The constant $L(t)$ above can be a polynomial of $t$.

Polynomial growth conjecture. The constant $D(t)$ above can be a polynomial of $t$.

Let $S$ be a surface, and let $T^1S$ carry a convex foliated $\mathbb{RP}^3$-structure. Its holonomy is allowed to lie in an arbitrary subgroup of…

Hitchin's conjecture. The space $\mathcal{H}_3$ is the space of conjugacy classes of monodromy representations of flat properly convex projective structures.

Let $G\cong\mathsf{PGL}(3,\mathbb{R})\cong\mathsf{SL}(3,\mathbb{R})$, and let $\mathfrak{C}(\Sigma)$ denote the deformation space of marked convex $\mathbb{R}\mathsf{P}^2$-structur…