6 problems

Let $D\subset\mathbb R^3$ be a convex set, and call a scaled and translated copy of $D$ without rotation a homothetic copy of $D$. Let $S$ be a finite set of points in…

Let $\mathcal A$ be a pseudo-disk arrangement, and let its members be the objects to be colored. The dual pseudo-disk arrangement conjecture. The members of any pseudo-disk arrange…

Let $\mathcal A$ be a pseudo-disk arrangement, meaning a family of planar bodies whose boundaries are Jordan curves and such that the boundary of any member intersects the boundary…

Let $D$ be a convex set in the plane, and call a scaled and translated copy of $D$ without rotation a homothetic copy of $D$. Let $S$ be a finite set of points. The three-color hom…

Let $D$ be a convex set in the plane, let $S$ be a finite set of points, and let $m$ be a positive integer. Pach's conjecture. For every convex set $D$ there is an $m$ such that an…

Let $\mathcal F$ be a family of pseudo-disks in the plane, let $S$ be a finite set of points, and let $m$ be a positive integer. The three-color pseudo-disk conjecture. If…