On July 14, 2026, Yaobin Chen from the IBS Extremal Combinatorics and Probability Group gave a talk at the Discrete Math Seminar on the maximum size of a subset in general position of a random subset of a finite-dimensional vector space over a finite field. The title of his talk was “Maximum in-general-position set in a random subset of $\mathbb{F}_q^d$“.
The IBS Discrete Mathematics Group welcomes Dr. Yaobin Chen and Dr. Simón Piga, new research fellows at the IBS Extremal Combinatorics and Probability Group, starting July 1, 2026.
Yaobin Chen received his Ph.D. from Fudan University under the supervision of Prof. Hehui Wu. He is interested in extremal graph theory and combinatorics.
Simón Piga received his Ph.D. from the University of Hamburg under the supervision of Prof. Mathias Schacht. Until recently, he was a postdoctoral researcher at the Czech Academy of Sciences. He is interested in extremal and probabilistic combinatorics.
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.
