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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Partial associativity and rough approximate groups
- William Timothy Gowers (University of Cambridge
)
DTSTART;TZID=Europe/London:20200316T100000
DTEND;TZID=Europe/London:20200316T110000
UID:TALK140605AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/140605
DESCRIPTION:Let X be a finite set and let o be a binary operat
ion on X that is injective in each variable separa
tely and has the property that

x o (y o z) = (
x o y) o z for a positive proportion of triples (x
\,y\,z) with x\,y\,z in X. What can we say about t
his operation? In particular\, must there be some
underlying group structure that causes the partial
associativity? The answer turns out to be yes ? u
p to a point. I shall explain what that point is a
nd give some indication of the ideas that go into
the proof\, which is joint work with Jason Long. I
shall also report on a natural strengthening that
one might hope for. We identified a likely counte
rexample\, which was recently proved to be a count
erexample by Ben Green\, so in a certain sense our
result cannot be improved. (However\, there are s
till some interesting questions one can ask.)

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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