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Non-abelian arithmetic combinatorics and diophantine approximation

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  • UserEmmanuel Breuillard (University of Paris-Sud)
  • ClockTuesday 27 September 2016, 15:00-16:00
  • HouseCMS, MR12.

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In the last ten years additive combinatorics has spread to group theory yielding a series of structure theorems for approximate subgroups, i.e. subsets that do not grow much under multiplication. Metric versions of these results, where one looks at the size of a set at various small scales, have also been developed shedding new light on the structure of dense subgroups of Lie groups. In parallel a theory of diophantine approximation on Lie groups is taking shape, and when combined with the former yields applications to spectral gap bounds, fast mixing of random walks, uniform exponential growth, Bernoulli convolutions and more. I will survey some these developments.

This talk is part of the Special DPMMS Colloquium series.

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