Algebraic Graph Theory: Group Theory and the Erdős-Ko-Rado (EKR) Theorem

Talk by Karen Meagher.

Group theory can be a key tool in solving problems in combinatorics; it can provide a clean and effective proofs, and it can give deeper understanding of why certain combinatorial results hold. My research has focused on the famous Erdős-Ko-Rado (EKR) Theorem theorem. There are many proofs, extensions and generalization of this result. My favourite proofs are the ones that make use of finite groups, particularly automorphism groups. In this talk I will give some background on the EKR theorem and show some of the extensions and generalizations of this theorem. I will go over some of the different proofs, comparing the older methods with the newer ones that make use of group theory. Finally, I will give more details about the EKR theorem for permutation groups, where the role of group theory is profound.