The previous talk in the series is here. The next talk in the series is here.
In the previous video I formulated the cap-set problem and proved a lemma about the so-called slice rank of a 3-tensor. In this video I show how to combine the slice-rank lemma with a clever use of polynomials to obtain an exponentially small upper bound for the cap-set problem: that is, there is a constant C < 3 such that any set of at least Cn points in 𝔽3n must contain distinct points x, y and z such that x + y + z = 0.
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.