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SUMMARY:Partial associativity and rough approximate groups - William Timot
 hy Gowers (University of Cambridge)
DTSTART:20200316T100000Z
DTEND:20200316T110000Z
UID:TALK140605@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Let X be a finite set and let o be a binary operation on X tha
 t is injective in each variable separately and has the property that <br>x
  o (y o z) = (x o y) o z for a positive proportion of triples (x\,y\,z) wi
 th x\,y\,z in X. What can we say about this operation? In particular\, mus
 t there be some underlying group structure that causes the partial associa
 tivity? The answer turns out to be yes ? up to a point. I shall explain wh
 at that point is and give some indication of the ideas that go into the pr
 oof\, which is joint work with Jason Long. I shall also report on a natura
 l strengthening that one might hope for. We identified a likely counterexa
 mple\, which was recently proved to be a counterexample by Ben Green\, so 
 in a certain sense our result cannot be improved. (However\, there are sti
 ll some interesting questions one can ask.)<br>
LOCATION:Seminar Room 1\, Newton Institute
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