Affiliation: University of Regina, Saskatchewan

**Title: A Brief Introduction to World of Erd\H{o}s-Ko-Rado Theorems**

**Abstract**: The Erd\H{o}s-Ko-Rado (EKR) theorem is a famous result that is one of the cornerstones of extremal set theory. This theorem answers the question “What is the largest family of intersecting sets, of a fixed size, from a base set?”

The talk is available here, and you can view the slides here.

*This talk was given on June 28th, 2022*

**Title: Group Theory and the Erd\H{o}s-Ko-Rado (EKR) Theorem**

**Abstract**: Group theory can be a key tool in sovling 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 Erd\H{o}s-Ko-Rado (EKR) 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 profound.

You can watch the talk here.

*This talk was given on July 20th, 2020*