Dr. Travis Johnston

Event Details

Title: Turán Problems on Hypergraphs

Abstract: What has become known as Turán problems are those of the following flavor: given a graph (or r-uniform hypergraph) H, how many edges can a host graph G have if it doesn’t contain H as a subgraph? This question has been widely studied. Turán, and later Erdös, Stone, and Simonovits, answered the question for simple graphs. However, determining the Turán density of even 3-uniform hypergraphs has proved to be very difficult.

In this talk we introduce problems on Turán problems on non-uniform hypergraphs. We extend several classical results for uniform hypergraphs. Additionally, we demonstrate how results about the Turán density of non-uniform hypergraphs can be applied to related problems involving forbidden subposets. This is joint work with my advisor Linyuan Lu.