The PIMS Postdoctoral Fellow Seminar: Felix Christian Clemen

A classical problem in combinatorial geometry, posed by Erd\H{o}s in 1946, asks to determine the maximum number of unit segments in a set of $n$ points in the plane. Since then a great variety of extremal problems in finite point sets have been studied. Here, we look at generalizations of this question concerning regular simplices. Among others we answer the following question asked by Erd\H{o}s: Given $n$ points in $\mathbb{R}^6$, how many triangles can be equilateral triangles? For our proofs we use hypergraph Tur\'an theory. This is joint work with Dumitrescu and Liu.