The previous talk in the series is here. The next talk in the series is here.
Let ℱ be a family of subsets of {1,2,…,n} such that every set in ℱ has size that satisfies some congruence condition mod p and every intersection of two distinct sets in ℱ fails to satisfy that condition. How large can ℱ be? The Frankl-Wilson theorem addresses this question and has had a large number of applications. In this video a special case of the theorem is proved, with a more modern proof that is simpler than that of Frankl and Wilson. As with the previous video, the main tool is a dimension argument.
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.