4 problems

Let $d,r$ be positive integers and let $k$ be a non-negative integer. A Tverberg $(r+1)$-partition of a finite point set is a partition into $r+1$ parts whose convex hulls have a c…

Sierksma's Dutch cheese conjecture. There are at least $((r-1)!)^d$ partitions of $X$ into parts whose convex hulls intersect. The conjecture extends the Dutch cheese conjecture fr…

Classification conjecture. For every Tverberg type $\mathcal I$, if $\mathcal I$ is colorful, then $\operatorname{Tv}_{\mathcal I}$ is unavoidable; otherwise,…

Let $q\geq 2$ be a prime power, $d\geq 1$, and let $G$ be a graph on $(d+1)(q-1)+1$ vertices. A graph is a $(d,q)$--Tverberg graph if it has the corresponding Tverberg property for…