An improved sunflower bound.

Computer Science/Discrete Mathematics Seminar I
Topic:An improved sunflower bound.
Speaker:Jiapeng Zhang
Affiliation:Harvard University
Date:Monday, October 7
Time/Room:11:00am - 12:00pm/Simonyi Hall 101
Video Link:https://video.ias.edu/csdm/2019/1007-JiapengZhang

A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all. Erdos and Rado in 1960 proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must contain a sunflower. The famous sunflower conjecture is that the bound on the number of sets can be improved to $c^w$ for some constant $c$. Despite much research, the best bounds until recently were all of the order of $w^{cw}$ for some constant c. In this work, we improve the bounds to about $(log w)^w$. Joint work with Ryan Alweiss, Shachar Lovett and Kewen Wu.