BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY: Large Sum-free sets via L^1-estimates - Benjamin Bedert (Cambridg
 e)
DTSTART:20251204T143000Z
DTEND:20251204T153000Z
UID:TALK240556@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:A set B is said to be sum-free if there are no x\,y\,z in B wi
 th x+y=z. A classical probabilistic argument of Erdös shows that any set 
 of N integers contains a sum-free subset of size N/3\, and this was later 
 improved to (N+1)/3 by Alon and Kleitman\, and then to (N+2)/3 by Bourgain
  using an elaborate Fourier-analytic approach. We show that there exists a
  constant c>0 such that any set of N integers contains a sum-free subset o
 f size N/3+c log log N\, confirming the longstanding suspicion that the 2/
 3 in Bourgain's bound can be improved to any large constant C (for large N
 ). A key step in the proof consists of establishing inverse results giving
  combinatorial descriptions for sets of integers whose Fourier transform h
 as small L^1-norm.
LOCATION:MR12
END:VEVENT
END:VCALENDAR