Combinatorics and Optimization reading group | Arkaprava Choudhury, Proof of the Sunflower Conjecture

Abstract: A $k$-sunflower is a family of $k$ distinct sets whose pairwise intersections all coincide. The Erd\H{o}s--Szemer\'edi conjecture asserts that for every $k \ge 3$ there is a constant $c_k < 2$ such that any $k$-sunflower-free family $\mathcal{F} \subseteq 2^{[n]}$ satisfies $|\mathcal{F}| \le c_k^{\,n}$. Bucic, He, and Lee recently proved this with an explicit bound.

In this talk we survey the problem and its place among sunflower questions, then work through the proof, centered on a vector-sunflower argument. We also discuss how the result relates to a related problem, the uniform Erd\H{o}s--Rado conjecture, which it does not settle. No prior background is assumed.