Lecture 4: Approximate Groups and the Bourgain-gamburd Method (preliminary Version)
نویسنده
چکیده
Up until the Bourgain-Gamburd 2005 breakthrough the only known ways to turn SLd(Fp) into an expander graph (i.e. to find a generating set of small size whose associated Cayley graph has a good spectral gap) was either through property (T ) (as in the Margulis construction) when d > 3 or through the Selberg property (and the dictionary between combinatorial expansion of the Cayley graphs and the spectral gap for the Laplace-Beltrami Laplacian on towers of covers of hyperbolic manifolds) when d = 2.
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