Growth in groups: an approach via incidence

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• Harald Helfgott (Bristol)
• Tuesday 23 January 2007, 16:30-17:30
• MR4, CMS.

If you have a question about this talk, please contact Ben Green.

Let K be R, C or a Z/pZ. Let G = SL_2(K). Not long ago, I proved the following theorem: for every subset A of G that is not contained in a proper subgroup, the set A\cdot A\cdot A is much larger than A. A generalisation to groups of higher rank was desired by many, but seemed hard to obtain.

I shall now present a proof somewhat different from the first one. The role of both the linearity and the group structure of G should now be clearer. A few ideas towards a generalisation will be discussed, with a focus on the case of SL_3(Z/pZ).

This talk is part of the Discrete Analysis Seminar series.

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