Georgia Institute of Technology College of Sciences

Given an $r$-uniform hypergraph $H$, the random Turán number $\mathrm{ex}(G^r_{n,p},H)$ is the maximum number of edges in an $H$-free subgraph of $G^r_{n,p}$, where $G^r_{n,p}$ is the Erdős-Rényi random hypergraph with parameter $p$. In the case when $H$ is not r-partite, the problem has been essentially solved independently by Conlon-Gowers and Schacht. In the case when $H$ is $r$-partite, the degenerate case, only some sporadic results are known.

The Sidorenko conjecture is a notorious problem in extremal combinatorics. It is known that its hypergraph analog is not true. Recently, Conlon, Lee, and Sidorenko discovered a relation between the Sidorenko conjecture and the Turán problem. 

 In this talk, we introduce some recent results on the degenerate random Turan problem and its relation to the hypergraph analog of the Sidorenko conjecture.