Sidorenko Hypergraphs and Random Turan Numbers

Start Date: December 6, 2023
Event Start Time: 12:15 PM
Event End Time: 1:15 PM
Seminar Series: Graduate Combinatorics Seminar
Presenter(s): Sam Spiro - Rutgers University
Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
Presentation Type: Stand Alone Presentation
Abstract:

Let $\mathrm{ex}(G_{n,p}^r,F)$ 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 $\mathrm{ex}(G_{n,p}^r,F)$ whenever $F$ is not Sidorenko. This connection between Sidorenko's conjecture and random Turan problems gives new lower bounds on $\mathrm{ex}(G_{n,p}^r,F)$ whenever $F$ is not Sidorenko, and further allows us to bound how \`\`far'' from Sidorenko an $r$ -graph $F$ is whenever upper bounds for $\mathrm{ex}(G_{n,p}^r,F)$ are known.
This is joint work with Jiaxi Nie.

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