Workshop on Additive Combinatorics and Algebraic Connections

G-stable Rank and the Cap Set Problem

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.

Date & Time

October 26, 2022 | 11:15am – 12:15pm

Location

Simonyi 101 and Remote Access

Speakers

Harm Derksen

Speaker Affiliation

Northeastern University

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