8 problems

Let $Z^c$ be the square grid circle pattern with $0<c<2$, whose circles are labeled by … and which covers the infinite sector with angle $c\pi/2$, with the centers of the border ci…

Let $0<\alpha=\beta<\frac{1}{2}$ and set $\gamma=1-2\alpha$, so that $0<\gamma<1$. Consider the hexagonal circle patterns $z^{3\alpha}$ with an intersection point at the origin and…

Let $S$ be a closed, oriented surface of genus at least $2$. An admissible weighted graph $(\Gamma,\theta)$ in $S$ is a graph embedded in $S$ that is the 1-skeleton of a cell decom…

Ideal circle-pattern uniformization conjecture. The following statements are equivalent: the combinatorial Ricci flow on $\mathcal{T}$ converges for every initial value in hyperbol…

Let $P(\Theta)$ be the space of circle patterns with a fixed Delaunay angle structure $\Theta$, let $P(S_g)$ be the space of marked complex projective structures, and let…

Let $S_g$ be a closed surface of genus $g$, let $E$ be the edge set of a triangulation of $S_g$, and let $\Theta:E\to[0,\pi)$ be a Delaunay angle structure. Let $P(\Theta)$ be the…

Generalized Andreev conjecture. There exists a compact convex hyperbolic polyhedron $Q$ combinatorially equivalent to $P$ whose dihedral angles are given by $\Theta$, and $Q$ is un…

Let $Q^{\mathbb{C}}(\operatorname{cr})$ and $Q^{\mathbb{R}}(\operatorname{cr})$ denote the complex and real spaces of discrete holomorphic quadratic differentials associated with a…