The ACO Seminar (2026–2027)

Tverberg’s theorem from 1966, also known as the affine Tverberg theorem, determines the minimal number of points in R^d needed to guarantee a partition into r parts whose convex hulls have a non-empty common intersection. The admissible-prescribable conjecture, essentially proved by Pór, aims to characterize the part sizes in such r-partitions for sufficiently large number of points. We prove the existence of counterexamples to the topological version of this conjecture. The talk is based on joint work with Pavle Blagojević and Florian Frick.