Affine Sieve and Expanders
نویسنده
چکیده
This note is based on my talk in the hot topics workshop at MSRI. My goals are to (1) Describe affine sieve: its most general setting and the fundamental theorem in the subject. (2) Convey the main ideas behind the proof of the fundamental theorem of affine sieve and its connection with expansion in linear groups. (3) Give a survey of some of the results on the expansion in linear groups and briefly explain what goes into their proofs. (4) Finish with some remarks, questions and conjectures.
منابع مشابه
Expanders and the Affine Building of Spn
For n ≥ 2 and a local field K, let ∆n denote the affine building naturally associated to the symplectic group Spn(K). We compute the spectral radius of the subgraph Yn of ∆n induced by the special vertices in ∆n, from which it follows that Yn is an analogue of a family of expanders and is non-amenable.
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For n ≥ 2 and a local field K, let ∆n denote the affine building naturally associated to the symplectic group Spn(K). We compute the spectral radius of the subgraph Yn of ∆n induced by the special vertices in ∆n, from which it follows that Yn is an analogue of a family of expanders and is non-amenable.
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