Expansion in Finite Simple Groups of Lie Type

By: Terence Tao

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Hardcover | 30 June 2015

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Hardcover
303 Pages

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25.4 x 17.8

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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.

Industry Reviews

Asymptotic group theory is a recently emerging branch of group theory, that can be described as the study of groups whose order is finite-but large! Tao's book is certainly a valuable introduction to that exciting new subject." - Alain Valette, Jahresbericht der Deutschen Mathematiker-Vereinigung

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