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The structure of approximate Abelian groups
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In this talk we shall look at the structure of sets that partially satisfy the axioms of an Abelian group. Specifically, we shall look at sets $A$ for which the proportion of triples $x,y,z \in A$ having $x+y-z \in A$ is at least $\delta$. (If $\delta =1$ then such sets are genuine cosets; for smaller $\delta$ we think of them as partial cosets.) A description of these sets is given by Freiman’s theorem, and our goal is to cover some recent improvements in this result. The talk is intended to be accessible, and will cover examples as well as what Freiman’s theorem is and why it is important.’
This talk is part of the Special DPMMS Colloquium series.
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