Exact Turán densities of hypergraphs

Determine the exact Turán density \(\pi(F)\) for arbitrary \(k\)-uniform hypergraphs \(F\) with \(k\geq 3\).

Background

The paper introduces the classical Turán density $\pi(F)$ of a $k$-uniform hypergraph as the asymptotic maximum edge density of an $F$-free $k$-graph. It explicitly identifies determining these values for general hypergraphs of uniformity at least three as a longstanding central problem in extremal combinatorics. This issue is presented as background motivating the study of the related codegree Turán density, rather than as a problem resolved by the paper.