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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Proving theorems inside sparse random sets - Gower
s\, WT (Cambridge)
DTSTART;TZID=Europe/London:20110331T100000
DTEND;TZID=Europe/London:20110331T110000
UID:TALK30494AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/30494
DESCRIPTION:In 1996 Kohayakawa\, Luczak and Rdl proved that Ro
th's theorem holds almost surely inside a subset o
f {1\,2\,...\,n} of density Cn^{-1/2}. That is\, i
f A is such a subset\, chosen randomly\, then with
high probability every subset B of A of size at l
east c|A| contains an arithmetic progression of le
ngth 3. (The constant C depends on c.) It is easy
to see that the result fails for sparser sets A. R
ecently\, David Conlon and I found a new proof of
this theorem using a very general method. As a con
sequence we obtained many other results with sharp
bounds\, thereby solving several open problems. I
n this talk I shall focus on the case of Roth's th
eorem\, but the generality of the method should be
clear from that.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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