Leírás
A sunflower is a set system, in which the intersection of every pair of distinct sets is the same. Erdos and Rado (1960) proved that if a family contains more than w!(p-1)^w size-w sets, then it contains a sunflower consisting of p sets. They also showed that the statement is false for some families of (p-1)^w size-w sets and conjectured that it should be true for c_p^w size-w sets, where c_p is some constant depending only on p.
The lower and upper bounds were hardly improved till last year, not even for the first non-trivial case of p=3. Then a breakthrough result of Ryan Alweiss, Shachar Lovett, Kewen Wu and Jiapeng Zhang improved the Erdos-Rado upper bound to something close to (but not achieving) the conjectured lower bound.
The talk is mostly based on the simplified proof of Anup Rao. Disclaimer: I have no involvement, just thought that such a nice result should be presented in the combinatorics seminar.