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Expansion in Finite Simple Groups of Lie Type

About this Title

Terence Tao, University of California, Los Angeles, CA

Publication: Graduate Studies in Mathematics
Publication Year: 2015; Volume 164
ISBNs: 978-1-4704-2196-0 (print); 978-1-4704-2265-3 (online)
DOI: https://doi.org/10.1090/gsm/164
MathSciNet review: MR3309986
MSC: Primary 20D06; Secondary 05C25, 05C81, 11B30, 17B20, 20F65, 20G30, 22D10

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Table of Contents

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Front/Back Matter

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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