10 problems

Let $\operatorname{Conf}_n$ be the configuration space of $n$ disks, and for $2\leq k\leq n$ let $\Delta_k\subset\operatorname{Conf}_n$ be the locus where at least $k$ points are c…

Let $\underline{m}$ be a finite multiset of component sizes, and let $r_{\min}(\underline{m})$ and $r_{\max}(\underline{m})$ denote the corresponding injectivity and nonvanishing t…

Let $\operatorname{Conf}_n$ be the configuration space of $n$ disks, and let $H^{\underline{m}}(\operatorname{Conf}_n)$ be the subspace of cohomology generated by ordered forests w…

Let $\operatorname{Conf}_n$ be the configuration space of $n$ disks, let $\operatorname{Conf}_{n,r}$ be the subspace in which the disks have radius at least $r$, and let…

Uniqueness conjecture. The uniqueness theorem for thin triangulated disk configurations remains true without the thinness requirement: every triangulated disk configuration is dete…

Let $\mathcal{C}$ be a disk configuration locally finite in $\mathbb{G}$, where $\mathbb{G}$ is one of $\hat{\mathbb{C}}$, $\mathbb{C}$, or $\mathbb{H}^2$, and let $(G,\Theta)$ be…

Let $\mathcal{C}$ and $\tilde{\mathcal{C}}$ be disk configurations, both locally finite in an ambient space $\mathbb{G}$ equal to either $\mathbb{C}$ or $\mathbb{H}^2$, realizing t…

Let $\mathcal{C}$ and $\tilde{\mathcal{C}}$ be disk configurations, locally finite in $\mathbb{G}$ and $\tilde{\mathbb{G}}$, respectively, where each ambient space is either…

Let $\mathcal{D}$ and $\tilde{\mathcal{D}}$ be disk configurations in $\mathbb{C}$ realizing the same incidence data. Let $\phi:\partial\mathcal{D}\to\partial\tilde{\mathcal{D}}$ b…

Let $\mathcal{C}$ and $\tilde{\mathcal{C}}$ be disk configurations satisfying the hypotheses of the paper's main rigidity and uniformization theorems, except that the thinness cond…