David James : A Weighted Hypergraph Turán Problem

Posted by Vishesh Jain , part of the Mathematical Computer Science Seminar.

At

March 16, 2026, 3 p.m.

In

1227 SEO

Abstract

A weighted hypergraph G is (F, r)-free if any copy of F in G has weight less than r. The weighted Turán number is the maximum weight of an (F, r)-free hypergraph on n vertices. Let H be the 3-graph {abc, abd, cde}. In a paper of Keevash and Mubayi, the asymptotic behavior, exact results for large n, and stability theorems of H-free hypergraphs are proven. We generalize all such results to (H, r)-free weighted hypergraphs for all values of r. These are the first such results for hypergraphs.