# MUIC Math

Mathematics at MUIC

### Internal

seminar:ew_cap_set

# The Cap Set Problem

Elaine Wong
Science Division, Mahidol University International College, Thailand

### Abstract

In this talk, we give some background and present a recent result of Croot, Lev, Pach, Ellenberg and Gijswijt on the cap set problem, which significantly improves the upper bound on the maximal size of a cap set in $F_3^n$ where F is a finite field using a novel method. While previous improvements on upper bounds were obtained using Fourier Methods (a la Roth and others), the proof of Croot et al. had stunned mathematicians earlier this year with its simplicity and only requires some basic understanding of linear algebra and a casual interest in the game of Set.