8 problems

Let $P$ be a strictly convex polygon in $\mathbb{RP}^d$. Suppose that $P$ intersects a hyperplane with multiplicity $k$, where $k\geq d+2$. Call a vertex configuration a flattening…

Let $P$ be an embedded closed polygon in $S^2$ that bisects the area, and call a vertex configuration a flattening when it has the polygonal analogue of an inflection point. Discre…

Let $P$ be an embedded non-contractible closed polygon in $\mathbb{RP}^2$, and call a vertex configuration a flattening when it has the polygonal analogue of an inflection point. D…

Let $W$ denote the conformal energy of a simplicial Willmore sphere. Quantization conjecture. The conformal energy is quantized: … This conjecture is motivated by numerical experim…

Doyle's conjecture. There are no locally univalent circle packings of the hexagonal triangulation $\mathcal{T}_H$ other than regular hexagonal packings and Doyle spirals.

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…

Let $N\ge 6$. Recall that $\mathcal{M}_N$ is the configuration space of $N$-Kaleidocycles, $\pi_c:\mathcal{M}_N\to\mathbb{R}$ is the projection onto the $c$-axis, where $c=\cos\nu$…

Let an abstract triangulated sphere be realized in $\mathbb{R}^3$, and let $\operatorname{D}$ denote its discrete Dirac operator. A triangulated-sphere realization conjecture. Ever…