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Thin groups and superstrong approximation

Author: Emmanuel Breuillard; Hee Oh; Mathematical Sciences Research Institute (Berkeley, Calif.)
Publisher: Berkeley, CA : Mathematical Sciences Research Institute ; New York, NY : Cambridge University Press, 2014.
Series: Mathematical Sciences Research Institute publications, 61.
Edition/Format:   Print book : Conference publication : EnglishView all editions and formats
Summary:
"This is a collection of surveys and primarily expository articles focusing on recent developments concerning various quantitative aspects of 'thin groups.' There are discrete subgroups of semisimple Lie groups that are both big (Zariski dense) and small (of infinite covolume). This dual nature leads to many intricate questions. Over the past few years, many new ideas and techniques, arising in particular from  Read more...
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Genre/Form: Conference papers and proceedings
Congresses
Material Type: Conference publication
Document Type: Book
All Authors / Contributors: Emmanuel Breuillard; Hee Oh; Mathematical Sciences Research Institute (Berkeley, Calif.)
ISBN: 9781107036857 1107036852
OCLC Number: 868037886
Notes: Based on the workshop "Thin Groups and Super-strong Approximation, '' held at Mathematical Sciences Research Institute, February 6th through 10th, 2012.
Description: xii, 362 pages : illustrations ; 24 cm.
Contents: Some Diophantine applications of the theory of group expansion --
A brief introduction to approximate groups --
Superstrong approximation for monodromy groups --
The ubiquity of thin groups --
The orbital circle method --
Sieves in discrete groups, expecially sparse --
How random are word maps? --
Constructing thin groups --
Ergodic properties of the Burger-Roblin measure --
Harmonic analysis, ergodic theory and counting for thin groups --
Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces --
Growth in linear groups --
Strong approximation for algebraic groups --
Generic phenomena in groups: some answers and many questions --
Affine sieve and expanders --
Notes on thin matrix groups.
Series Title: Mathematical Sciences Research Institute publications, 61.
Responsibility: edited by Emmanuel Breuillard, Universite Paris-Sud 11, Hee Oh, Yale University.

Abstract:

This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.  Read more...

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