Speaker: Jiaxi Nie  (Georgia Institute of Technology)

 

 

Abstract:Let \(\alpha(\mathbb{F}_q^{d},p)\) be the maximum possible size of a point set in general position in a \(p\)-random subset of \(\mathbb{F}_q^d\). We determine the order of magnitude of \(\alpha(\mathbb{F}_q^{d},p)\) up to a polylogarithmic factor by proving the balanced supersaturation conjecture of Balogh and Luo. Our result also resolves a conjecture implicitly posed by Chen, Liu, Zeng, and myself. This is joint work with Chen, Yu, and Zhang.