Georgia Institute of Technology College of Sciences

A successful trend in modern extremal/probabilistic combinatorics is the investigation of how well classical theorems, like those of Ramsey, Turán, and Szemerédi, hold in sparse random contexts. Graph and hypergraph container methods have played a big role in improving our knowledge of these sparse structures. I will present joint work with Jozsef Balogh and Haoran Luo on a random version of the Erdős-Ko-Rado Theorem and Sperner's Theorem, giving the flavor of some graph container techniques.