报告人：陈耀斌（复旦大学）

时 间：11月10日（周一），15:00—16:00

地 点：数学科学学院新楼 308

题 目：Maximum in-general-position set in a random subset of F_{q}^{d}

摘 要：

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, Nie 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.