ENGLISH

Expansion in Finite Simple Groups of Lie Type

By Terence Tao

Book information

Publisher
American Mathematical Society
Year
2015
ISBN
1470421968, 9781470421960
Language
english
Format
PDF
Filesize
2 MB (1986774 bytes)
Series
Graduate Studies in Mathematics 164
Edition
Draft
Pages
297\297
Time added
2015-10-18 06:45:21

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.

Similar books