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Expansion in Finite Simple Groups of Lie Type (Graduate Studies in Mathematics)

Penned By Terence Tao
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Expansion in Finite Simple Groups of Lie Type (Graduate Studies in Mathematics)

Penned By Terence Tao
4.85 81,720 Ratings
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Editor's Note:
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.

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Language Eng
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Identifier (ISBN) 39687111
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Terence Tao
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Terence Tao

After spending years working in the corporate world, Terence Tao finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Richard Hill
Richard Hill December 30, 2025
"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
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"A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend."
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Laura Carter
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"Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Unlikely to reread, but a reasonable expenditure of time."
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"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
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"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me."
Emily Nelson
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"I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
Dorothy Anderson
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"A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me."
Robert Phillips
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Daniel Adams
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"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall."
John  Parker
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"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
Andrew Anderson
Andrew Anderson February 13, 2024
"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
Kenneth Smith
Kenneth Smith November 07, 2025
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
Paul Brown
Paul Brown June 17, 2025
"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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James Cruz February 13, 2024
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Cynthia Adams February 12, 2024
"Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars."
Cynthia Thomas
Cynthia Thomas August 25, 2024
"It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average."
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"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
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