The Sunflower Problem

ACO Student Seminar
Friday, October 23, 2020 - 1:00pm for 1 hour (actually 50 minutes)
Tolson Bell – Math, Georgia Tech –
He Guo

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 breakthroughs within the last year 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), which we obtained during the 2020 REU at Georgia Tech. As time permits, I will elaborate on key lemmas and techniques used in recent improvements.

Based on joint work with Suchakree Chueluecha (Lehigh University) and Lutz Warnke (Georgia Tech), seeĀ