The ACO Seminar (2021–2022)

A sunflower with p petals consists of p sets whose pairwise intersections are all the same set. The goal of the sunflower problem is to find the smallest r = r(p,k) such that every family of at least r^k k-element sets must contain a sunflower with p petals. Major recent breakthroughs by Alweiss-Lovett-Wu-Zhang and others show that r = O(p log(pk)) suffices. In this talk, after reviewing the history and significance of the Sunflower Problem, I will present our improvement to r = O(p log k). As time permits, I will elaborate on key lemmas and techniques used in recent improvements. This is based on joint work with Suchakree Chueluecha (University of Virginia) and Lutz Warnke (Georgia Tech), see https://arxiv.org/abs/2009.09327.