Expansion in finite simple groups of Lie type

書誌事項

Expansion in finite simple groups of Lie type

Terence Tao

(Graduate studies in mathematics, v. 164)

American Mathematical Society, c2015

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注記

Includes bibliographical references (p. 293-300) and index

内容説明・目次

内容説明

Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemeredi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.

目次

Expansion in Cayley graphs Expander graphs: Basic theory Expansion in Cayley graphs, and Kazhdan's property (T) Quasirandom groups The Balog-Szemeredi-Gowers lemma, and the Bourgain-Gamburd expansion machine Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality Non-concentration in subgroups Sieving and expanders Related articles Cayley graphs the algebra of groups The Lang-Weil bound The spectral theorem and its converses for unbounded self-adjoint operators Notes on Lie algebras Notes on groups of Lie type Bibliography Index

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詳細情報

  • NII書誌ID(NCID)
    BB18565724
  • ISBN
    • 9781470421960
  • LCCN
    2014049154
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Providence, R.I.
  • ページ数/冊数
    xiii, 303 p.
  • 大きさ
    27 cm
  • 分類
  • 件名
  • 親書誌ID
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