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SUMMARY:Proving theorems inside sparse random sets - Gowers\, WT (Cambridg
 e)
DTSTART:20110331T090000Z
DTEND:20110331T100000Z
UID:TALK30494@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In 1996 Kohayakawa\, Luczak and Rdl proved that Roth's theorem
  holds almost surely inside a subset of {1\,2\,...\,n} of density Cn^{-1/2
 }. That is\, if A is such a subset\, chosen randomly\, then with high prob
 ability every subset B of A of size at least c|A| contains an arithmetic p
 rogression of length 3. (The constant C depends on c.) It is easy to see t
 hat the result fails for sparser sets A. Recently\, David Conlon and I fou
 nd a new proof of this theorem using a very general method. As a consequen
 ce we obtained many other results with sharp bounds\, thereby solving seve
 ral open problems. In this talk I shall focus on the case of Roth's theore
 m\, but the generality of the method should be clear from that.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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