On the Erdős-Purdy problem and the Zarankiewitz problem for semialgebraic graphs

Nora Frankl, Andrey Kupavskii

Erdős and Purdy, and later Agarwal and Sharir, conjectured that any set of $n$ points in ${\mathbb{R}}^d$ determine at most $C{n}^{d/2}$ congruent $k$-simplices for even $d$. We obtai…