2026.07.14, Yaobin Chen, Maximum in-general-position set in a random subset of $\mathbb{F}^d_q$

Yaobin Chen, Maximum in-general-position set in a random subset of $\mathbb{F}^d_q$ July 14 Tuesday @ 4:30 PM - 5:30 PM KST Room B332, IBS (기초과학연구원) Yaobin Chen IBS Extremal Combinatorics and Probability Group https://sites.google.com/view/yaobinc... 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 the first author, Liu, the second author and Zeng. In the course of our proof, we establish a lemma that demonstrates a “structure vs. randomness” phenomenon for point sets in finite-field linear spaces, which may be of independent interest. This is joint work with Jiaxi Nie, Jing Yu, and Wentao Zhang.