5 problems

Let $\mathcal F$ be the family of bottomless rectangles in the plane, and let $m_k^*(\mathcal F)$ denote the corresponding threshold for decomposing coverings into $k$ coverings. B…

The $S_1$ extremal conjecture.

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…