Katona cycle methods and applications

Intersection problems are of great interest, and importance, in extremal combinatorics. The Erdos-Ko-Rado theorem is one of the most important results in intersection problems. In this talk, I will introduce Katona’s proof of Erdos-Ko-Rado theorem, which Erdos described as a ‘Book Proof’. Then I will show some further applications of Katona cycle methods in forbidden subposet problems. This is based on joint work of Casey Tompkins and Gyula Katona.