Thin Groups and Superstrong Approximation
Edited by Emmanuel Breuillard and Hee Oh
Contents
Front matter (front page, copyright page)
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Table of Contents
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Preface by Emmanuel Breuillard and Hee Oh, ix–xii
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Some Diophantine applications of the theory of group expansion by Jean Bourgain, 1–22
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A brief introduction to approximate groups by Emmanuel Breuillard, 23–50
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Superstrong approximation for monodromy groups by Jordan S. Ellenberg, 51–71
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The ubiquity of thin groups by Elena Fuchs, 73–92
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The orbital circle method by Alex Kontorovich, 93–106
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Sieves in discrete groups, especially sparse by Emmanuel Kowalski, 107–140
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How random are word maps? by Michael Larsen, 141–149
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Constructing thin groups by D. D. Long and A. W. Reid, 151–166
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Ergodic properties of the Burger–Roblin measure by Amir Mohammadi, 167–178
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Harmonic analysis, ergodic theory and counting for thin groups by Hee Oh, 179–210
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Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces
by Gopal Prasad and Andrei S. Rapinchuk, 211–252
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Growth in linear groups by László Pyber and Endre Szabó, 253–268
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Strong approximation for algebraic groups by Andrei S. Rapinchuk, 269–298
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Generic phenomena in groups: some answers and many questions by Igor Rivin, 299–324
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Affine sieve and expanders by Alireza Salehi Golsefidy, 325–342
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Notes on thin matrix groups by Peter Sarnak, 343–362
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