Product mixing and product-free sets in the alternating group

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• Sean Eberhard (University of Oxford)
• Thursday 03 March 2016, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

Abstract: There is an obvious product-free subset of the symmetric group of size 1/2, but what about for the alternating group? There is a natural example of density n^(-1/2 + o(1)). We’ll talk about why this is in fact the right answer, and how this fits in with a general ‘product mixing’ phenomenon. Our tools include some nonabelian Fourier analysis, a version of entropy subadditivity adapted to the symmetric group, and a concentration-of-measure result for rearrangements of inner products.

This talk is part of the Combinatorics Seminar series.

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