The previous talk in the series is here. The next talk in the series is here.
The main result discussed here is a beautiful proof by Gyula Katona of the Erdos-Ko-Rado theorem, which answers the following question: how many subsets of {1,2,…,n} of size k is it possible to pick if any two of them must intersect? First, we have the largest size of a general intersecting family, then intersecting families of k-sets and the Erdos-Ko-Rado theorem, and after the equality case.
This video was produced by Tim Gowers as part of his Part III course at the University of Cambridge. Printed notes for this course are available here.