Hypergraph Turan Problem
Hypergraph Turan Problem

Oleg Pikhurko, CarnegieMellon University
Fine Hall 224
The Turan function $ex(n,F)$ of a kgraph $F$ is the maximum number of edges in an $F$free kgraph on $n$ vertices. This problem goes back to the fundamental paper of Turan from 1941 that solved it for complete graphs (k=2). Unfortunately, very few nontrivial instances of the problem have been solved when we consider hypergraphs (k>2).We survey some recent results and methods on the hypergraph Turan function. In particular, we discuss the socalled stability approach that greatly helps in obtaining exact results from asymptotic computations (for example, those that use flag algebras or graph limits).