Description
Combinatorics Seminar.
Speaker: S. Venkatesh.
Affiliation: Department of Mathematics, IIT Bombay.
Date and Time: Wednesday 22 January, 11:00 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Improved Bounds for the Sunflower Lemma.
Abstract: For a positive integer r, an r-sunflower is a collection of r
finite sets such that the intersection of any two sets is the intersection
of all. The Erdos-Rado Sunflower conjecture states that for any fixed
positive integer r, there exists a constant c>0 such that the following
holds for eventually all positive integers w: for every collection of at
least c^w sets, each having size w, there exists a subcollection which is
an r-sunflower.
Erdos and Rado (1960), while posing the Sunflower conjecture, showed that
every collection with at least about w^w sets, each having size w, will
contain an r-sunflower. In this talk, we will see an improvement by
Alweiss, Lovett, Wu and Zhang (2019), who show that every collection with
at least about (log w)^w sets, each having size w, will contain an
r-sunflower.