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Expansion in Finite Simple Groups of Lie Type

Terence Tao University of California, Los Angeles, CA
Available Formats:
Hardcover ISBN: 978-1-4704-2196-0
Product Code: GSM/164
List Price: $84.00 MAA Member Price:$75.60
AMS Member Price: $67.20 Electronic ISBN: 978-1-4704-2265-3 Product Code: GSM/164.E List Price:$79.00
MAA Member Price: $71.10 AMS Member Price:$63.20
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List Price: $126.00 MAA Member Price:$113.40
AMS Member Price: $100.80 Click above image for expanded view Expansion in Finite Simple Groups of Lie Type Terence Tao University of California, Los Angeles, CA Available Formats:  Hardcover ISBN: 978-1-4704-2196-0 Product Code: GSM/164  List Price:$84.00 MAA Member Price: $75.60 AMS Member Price:$67.20
 Electronic ISBN: 978-1-4704-2265-3 Product Code: GSM/164.E
 List Price: $79.00 MAA Member Price:$71.10 AMS Member Price: $63.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$126.00 MAA Member Price: $113.40 AMS Member Price:$100.80
• Book Details

Volume: 1642015; 303 pp
MSC: Primary 05; 11; 20;

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–Szemerédi–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.

Graduate students and research mathematicians interested in graph theory, geometric group theory, and arithmetic combinatorics.

• Part 1. Expansion in Cayley graphs
• Chapter 1. Expander graphs: Basic theory
• Chapter 2. Expansion in Cayley graphs, and Kazhdan’s property (T)
• Chapter 3. Quasirandom groups
• Chapter 4. The Balog-Szemerédi-Gowers lemma, and the Bourgain-Gamburd expansion machine
• Chapter 5. Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality
• Chapter 6. Non-concentration in subgroups
• Chapter 7. Sieving and expanders
• Part 2. Related articles
• Chapter 8. Cayley graphs the algebra of groups
• Chapter 9. The Lang-Weil bound
• Chapter 10. The spectral theorem and its converses for unbounded self-adjoint operators
• Chapter 11. Notes on Lie algebras
• Chapter 12. Notes on groups of Lie type

• 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, Jahresber Dtsch Math-Ver
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1642015; 303 pp
MSC: Primary 05; 11; 20;

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–Szemerédi–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.

Graduate students and research mathematicians interested in graph theory, geometric group theory, and arithmetic combinatorics.

• Part 1. Expansion in Cayley graphs
• Chapter 1. Expander graphs: Basic theory
• Chapter 2. Expansion in Cayley graphs, and Kazhdan’s property (T)
• Chapter 3. Quasirandom groups
• Chapter 4. The Balog-Szemerédi-Gowers lemma, and the Bourgain-Gamburd expansion machine
• Chapter 5. Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality
• Chapter 6. Non-concentration in subgroups
• Chapter 7. Sieving and expanders
• Part 2. Related articles
• Chapter 8. Cayley graphs the algebra of groups
• Chapter 9. The Lang-Weil bound
• Chapter 10. The spectral theorem and its converses for unbounded self-adjoint operators
• Chapter 11. Notes on Lie algebras
• Chapter 12. Notes on groups of Lie type
• 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, Jahresber Dtsch Math-Ver
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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