Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 07, 2020, 12:15 pm

Duration: 45 minutes

Location: Zoom: conference room

Speaker: Miklós Horváth

On Improvements of the Sunflower Lemma

A family of p sets whose pairwise intersections are the same is called a p-sunflower. This talk is about finding the minimum f(p,k) such that any family of f(p,k) sets of cardinality k is guaranteed to contain a p-sunflower.

Erdős and Rado introduced this problem in 1960 and proved first bounds on f(p,k). In a recent breakthrough, Alweiss, Lovett, Wu and Zhang showed a significantly improved upper bound on f(p,k). Afterwards, Rao proved a similar upper bound with a cleaner proof [1], which is outlined in this talk.

[1] A. Rao, Coding for Sunflowers, Discrete Analysis, 2020

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