6 problems

A skew configuration is a set of pairwise non-intersecting, pairwise non-parallel lines in $\mathbb{R}^3$. A spindle is a skew configuration whose lines all intersect an oriented a…

Let $\mathrm{GR}(21_4)$ be the Grünbaum–Rigby configuration, decomposed into subconfigurations $\mathrm S_{12}$, $\mathrm S_{13}$, and $\mathrm S_{23}$ with point orbits…

Let $A\subset\mathbb{R}^2$ be a set of positive upper density, and let $u,v,w\in\mathbb{R}^2$ be non-collinear points. A configuration congruent to a finite set means an image of t…

Classification conjecture. A cyclic $(n_3)$ configuration is unsplittable if and only if its Levi graph belongs to one of the following three infinite families:

An $n_3$-configuration is a $3$-uniform configuration with $n$ points and $n$ lines, in which every point lies on three lines and every line contains three points. Call such a conf…

Let Danzer's $(35_4)$ point-line configuration be the incidence configuration with 35 points and 35 lines, each point and line incident with four objects. A geometric point-line re…