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Look Inside Thin Groups and Superstrong Approximation

Thin Groups and Superstrong Approximation

AUD$136.95 inc GST

Part of Mathematical Sciences Research Institute Publications

Jean Bourgain, Emmanuel Breuillard, Jordan S. Ellenberg, Elena Fuchs, Alex V. Kontorovich, Emmanuel Kowalski, Michael Larsen, Darren Long, Alan W. Reid, Amir Mohammadi, Hee Oh, Gopal Prasad, Andrei Rapinchuk, László Pyber, Endre Szabó, Andrei Rapinchuk, Igor Rivin, Alireza Salehi Golsefidy, Peter Sarnak
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  • Date Published: February 2014
  • availability: Available
  • format: Hardback
  • isbn: 9781107036857

AUD$ 136.95 inc GST
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About the Authors
  • This collection of survey and research articles focuses on recent developments concerning various quantitative aspects of 'thin groups'. There are discrete subgroups of semisimple Lie groups that are both big (i.e. Zariski dense) and small (i.e. of infinite co-volume). This dual nature leads to many intricate questions. Over the past few years, many new ideas and techniques, arising in particular from arithmetic combinatorics, have been involved in the study of such groups, leading, for instance, to far-reaching generalizations of the strong approximation theorem in which congruence quotients are shown to exhibit a spectral gap, referred to as superstrong approximation. This book provides a broad panorama of a very active field of mathematics at the boundary between geometry, dynamical systems, number theory and combinatorics. It is suitable for professional mathematicians and graduate students in mathematics interested in this fascinating area of research.

    • Describes the most recent advances in an exciting subject that has developed very rapidly in recent years
    • Gathers a collection of well-written surveys by the best experts in the field
    • Includes an overview of the field by Peter Sarnak, Institute of Advanced Study, Princeton
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    Product details

    • Date Published: February 2014
    • format: Hardback
    • isbn: 9781107036857
    • length: 376 pages
    • dimensions: 234 x 156 x 22 mm
    • weight: 0.7kg
    • availability: Available
  • Table of Contents

    1. Some Diophantine applications of the theory of group expansion Jean Bourgain
    2. A brief introduction to approximate groups Emmanuel Breuillard
    3. Superstrong approximation for monodromy groups Jordan S. Ellenberg
    4. The ubiquity of thin groups Elena Fuchs
    5. The orbital circle method Alex V. Kontorovich
    6. Sieve in discrete groups, especially sparse Emmanuel Kowalski
    7. How random are word maps? Michael Larsen
    8. Constructing thin groups Darren Long and Alan W. Reid
    9. On ergodic properties of the Burger-Roblin measure Amir Mohammadi
    10. Harmonic analysis, ergodic theory and counting for thin groups Hee Oh
    11. Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces Gopal Prasad and Andrei Rapinchuk
    12. Growth in linear groups László Pyber and Endre Szabó
    13. On strong approximation for algebraic groups Andrei Rapinchuk
    14. Generic phenomena in groups: some answers and many questions Igor Rivin
    15. Affine sieve and expanders Alireza Salehi Golsefidy
    16. Growth in linear groups Peter Sarnak.

  • Editors

    Emmanuel Breuillard, Université de Paris XI
    Emmanuel Breuillard is a Professor at the Laboratoire de Mathématiques, Université Paris-Sud Orsay. He was recently awarded an EMS Prize by the European Mathematical Society for his work in group theory.

    Hee Oh, Yale University, Connecticut
    Hee Oh is a Professor of Mathematics at Brown University. She is an inaugural Fellow of the American Mathematical Society and has given a joint AMS-MAA invited address at the 2012 Joint Mathematics meetings and an invited lecture at the International Congress of Mathematicians in 2010.

    Contributors

    Jean Bourgain, Emmanuel Breuillard, Jordan S. Ellenberg, Elena Fuchs, Alex V. Kontorovich, Emmanuel Kowalski, Michael Larsen, Darren Long, Alan W. Reid, Amir Mohammadi, Hee Oh, Gopal Prasad, Andrei Rapinchuk, László Pyber, Endre Szabó, Andrei Rapinchuk, Igor Rivin, Alireza Salehi Golsefidy, Peter Sarnak

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