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An introduction to discrete approximate subgroups of Lie groups

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If you have a question about this talk, please contact Aled Walker.

In the first part of this talk I will introduce various methods (geometric, dynamical, analytical) to study infinite discrete approximate subgroups of Lie groups and briefly survey some of the results obtained in this area over the last few years (jointly with Michael Björklund, Jean-Philippe Burelle, Matt Cordes, Fanny Kassel, Felix Pogorzelski, Vera Tonic, Stefan Witzel and others). A particular focus will be on uniform and non-uniform approximate lattices and their associated dynamical systems.

In the second part of this talk I will focus on a single theorem, the classical Borel density theorem on lattices in semisimple Lie groups, and explain the difficulties one has to face in extending this result to approximate lattices and how these can be overcome. This part is based on joint work with Michael Björklund and Thierry Stulemeijer.

This talk is part of the Discrete Analysis Seminar series.

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