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DTSTART:19700329T010000
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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Sets without four term progressions but rich in th
ree term progressions - Oliver Roche-Newton (RICAM
\, Linz\, Austria)
DTSTART;TZID=Europe/London:20190529T134500
DTEND;TZID=Europe/London:20190529T144500
UID:TALK122620AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/122620
DESCRIPTION:The main question that will be addressed in this t
alk is the following: given a set A which does not
contain any four term arithmetic progressions\, i
s it necessarily the case that there exists a larg
e subset of A which does not contain any three ter
m arithmetic progressions?\n\nPerhaps one might gu
ess that the answer is "yes"\, and that by deletin
g a relatively small number of elements from A we
can destroy all progressions. In fact this rough i
ntuition seems to be false\, as we aim to show in
this talk by constructing sets (in both the intege
rs and finite field setting) with no 4APs but for
which all large subsets contain a 3AP. Possible co
nnections with quantitative bounds for Roth's Theo
rem will also be discussed. The proof uses the met
hod of hypergraph containers.\n\nThis talk is base
d on joint work with Cosmin Pohoata
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Aled Walker
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