Speaker: Sam Spiro (Rutgers)

Title: Sidorenko Hypergraphs and Random Turan Numbers

Abstract: Let ex(G_{n,p}^r,F) denote the maximum number of edges in an F-free subgraph of the random r-uniform hypergraph G_{n,p}^r. Following recent work of Conlon, Lee, and Sidorenko, we prove non-trivial lower bounds on ex(G_{n,p}^r,F) whenever F is not Sidorenko. This connection between Sidorenko's conjecture and random Turan problems gives new lower bounds on ex(G_{n,p}^r,F) whenever F is not Sidorenko, and further allows us to bound how ``far'' from Sidorenko an r-graph F is whenever upper bounds for ex(G_{n,p}^r,F) are known. This is joint work with Jiaxi Nie.