Expansion in Finite Simple Groups of Lie Type

Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics. He is the James and Carol Collins Chair of mathematics at UCLA and the youngest person ever to be promoted to full professor at the age of 24. In 2006 Tao became the youngest ever mathematician to win the Fields Medal. His other honours include the George Polya Prize from the Society for Industrial and Applied Mathematics (2010), the Alan T Waterman Award from the National Science Foundation (2008), the SASTRA Ramanujan Prize (2006), the Clay Research Award from the Clay Mathematical Institute (2003), the Bocher Memorial Prize from the American Mathematical Society (2002) and the Salem Prize (2000).

Expansion in Cayley graphs
Expander graphs: Basic theory
Expansion in Cayley graphs, and Kazhdan's property (T)
Quasirandom groups
The Balog-Szemeredi-Gowers lemma, and the Bourgain-Gamburd expansion machine
Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality
Non-concentration in subgroups
Sieving and expanders
Related articles
Cayley graphs the algebra of groups
The Lang-Weil bound
The spectral theorem and its converses for unbounded self-adjoint operators
Notes on Lie algebras
Notes on groups of Lie type
Bibliography
Index