Ruth Luo, Induced Turán problems for hypergraphs

Let $F$ be a graph. We say that a hypergraph $\mathcal{H}$ is an induced Berge $F$ if there exists a bijective mapping $f$ from the edges of $F$ to the hyperedges of $\mathcal{H}$ such that for all $xy\in E(F)$, $f(xy)\cap V(F)=\{x,y\}$. In this talk, we show asymptotics for the maximum number of edges in $r$-uniform hypergraphs with no induced Berge $F$. In particular, this function is strongly related to the generalized Turán function $ex(n,K_r,F)$, i.e., the maximum number of cliques of size $r$ in $n$-vertex, $F$-free graphs.  Joint work with Zoltan Füredi.