9 problems

Let $\Sigma_g$ be a closed orientable surface of genus $g\geq 1$, and let $\tau$ be a graph on $\Sigma_g$ that lifts to a triangulation of the universal cover. Let…

Classification conjecture. Every projective structure with holonomy a singly degenerate group $\Gamma$ is one of the following: $\Sigma$; $\Sigma_{\mathcal{C}}$ for some collection…

Let $\Sigma_g$ be a closed surface of genus $g$, let $\tau$ be a triangulation of $\Sigma_g$, and let ${\mathcal C}_{\tau}$ be its circle-packing deformation space. Let…

Let $\Sigma_g$ be a closed surface of genus $g$, and let $\tau$ be a triangulation of $\Sigma_g$ whose lift to the universal cover is covered by a simple graph. Let…

Gaiotto's classification conjecture. Real opers are classified topologically by the real locus of their developing map.

Let $p(z)$ be a complex polynomial of degree $3$ with multiplicity $2$ at $0$, and let $L$ define the projective structure on $\frak{B}$ associated with the preceding construction.…

Finiteness conjecture. For every smooth projective variety $X$ over $k$ and every positive integer $N$, the set

Let $\rho_{t_0,s}$ be the representation obtained by bulging a real projective structure along a separating simple closed curve, with complementary subsurfaces corresponding to…

Nonexistence conjecture. There exists no positive integer solution $(k_1,\ldots,k_j)$ of this equation such that $k_i\leq b1-1$ for every $i$.