Thin groups and superstrong approximation
Author(s)
Bibliographic Information
Thin groups and superstrong approximation
(Mathematical Sciences Research Institute publications, 61)
Cambridge University Press, 2014
- : hardback
Available at 23 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackBRE||38||1200026150270
Note
"The workshop 'Thin Groups and Super-strong Approximation' was held at MSRI from February 6th through 10th, 2012."--Pref
Includes bibliographical references
Description and Table of Contents
Description
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.
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 Laszlo Pyber and Endre Szabo
- 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.
by "Nielsen BookData"