Author

Publication

2015 - American Mathematical Society, Providence, Rhode Island, Rhode Island

Language

English

Word Count

75,750 words, Guess

Page Count

303 pages

Identifiers

Classifications

  • DDC512/.482
  • LCCQA387 .T356 2015
  • LCCQA387.T356 2015

Description

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.

Subjects

Topics

Lie groupsFinite simple groupsCombinatorics -- Graph theory -- Random walks on graphsNumber theory -- Sequences and sets -- Arithmetic combinatorics; higher degree uniformityGroup theory and generalizations -- Representation theory of groups -- Representations of finite groups of Lie typeGroup theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie typeGroup theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over finite fields

Series Statement

  • Graduate studies in mathematics -- volume 164

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