The Erdős-Ko-Rado Theorem, generalisations and beyond

Abstract: 

Extremal Set Theory is a branch of Extremal Combinatorics where one characterises the maximum size of a family of sets with certain restriction on them. The Erdős-Ko-Rado Theorem is a classical result in Extremal Set Theory and since its discovery, it has been extensively researched and generalised. In this talk an introduction of the Erdős-Ko-Rado Theorem is given as well as some generalisations and analogous results for other structures such as vector spaces over a finite field. Open problems as well as new possible directions of research are given for a particular generalisation of the Erdős-Ko-Rado Theorem.