This talk is part of the Advances in Boolean Function Analysis Lecture Series. The series will feature weekly two-hour lectures that aim to address both the broad context of the result and the technical details. Though closely related in theme, each lecture will be self-contained. Join us weekly at 10:00 a.m. PDT, from July 15, 2020 to August 18, 2020. There is a five minute break at the end of the first hour.

Abstract:
A sunflower is a collection of sets whose pairwise intersections are all the same. Erdos and Rado proved the sunflower lemma: any large enough family of sets must contain a sunflower. In the same paper, they conjectured an improved bound, which became known as the "sunflower conjecture". In this talk, I will describe recent progress towards proving the conjecture. The proof builds upon a structure vs pseudo-randomness paradigm and a surprising connection to how DNFs (Disjunctive Normal Forms) simplify under random restrictions.

Joint work with Ryan Alweiss, Kewen Wu and Jiapeng Zhang.