The Erdos-Ko-Rado Theorem, Generalisations and Beyond

Extremal Set Theory is a branch of Extremal Combinatorics where one characterises the maximum size of a family of sets with certain restrictions on them. The Erdos-Ko-Rado Theorem is a classical result in Extremal Set Theory and since its discovery, it has been extensively researched and generalised, though many open problems still remain. It is a result on sets but many analogous results have arisen for other structures such as permutations and vector spaces over a finite field.

I will be talking in some detail about simple problems in Extremal Set Theory which motivate the Erdos-Ko-Rado Theorem, and I will also present generalisations and analogs. A particular generalisation gives rise to an interesting open problem, and I will present a result of my own related to this as well as some new questions which could be asked.