Workshop on Additive Combinatorics and Algebraic Connections

Abstract: Ellenberg and Gijswijt drastically improved the best known upper asymptotic bound for the cardinality of a cap set in 2016. Tao introduced the notion of slice rank for tensors and showed that the Ellenberg-Gijswijt proof can be nicely formulated using this concept. I will introduce another rank for tensors, the G-stable rank and how it can be used to modestly improve upper bounds for cap sets.  I will also discuss an improvement of the asymptotic bounds by Zhi Jiang.