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Lois Leveen: IMG Forsooth Me Not: Shakespeare, Juliet, Her Nurse, and a Novel



There's this writer, William Shakespeare. Perhaps you've heard of him. He wrote this play, Romeo and Juliet. Maybe you've heard of it as well. It's... Continue »
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    Juliet's Nurse

    Lois Leveen 9781476757445

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Discrete Groups, Expanding Graphs and Invariant Measures: Appendix by Jonathan D. Rogawski (Modern Birkhauser Classics)

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Discrete Groups, Expanding Graphs and Invariant Measures: Appendix by Jonathan D. Rogawski (Modern Birkhauser Classics) Cover

 

Synopses & Reviews

Publisher Comments:

The book presents the solutions to two problems: the first is the construction of expanding graphs - graphs which are of fundamental importance for communication networks and computer science; the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres. Both problems were partially solved using the Kazhdan property (T) from representation theory of semi-simple Lie groups. Later, complete soultions were obtained for both problems using the Ramanujan conjecture from analytic number theory. The author, who played an important role in these developments, explains the two problems and their solutions from a perspective which reveals why all these seemingly unrelated topics are so interconnected. The unified approach shows interrelations between different branches of mathematics such as graph theory, measure theory, Riemannian geometry, discrete subgroups of Lie groups, representation theory and analytic number theory. Special efforts were made to make the book accessible to graduate students in mathematics and computer science. A number of problems and suggestions for further research are presented. Reviews: "This exciting book marks the genesis of a new field. It is a field in which one passes back and forth at will through the looking glass dividing the discrete from the continuous. (...) The book is a charming combination of topics from group theory (finite and infinite), combinatorics, number theory, harmonic analysis." - Zentralblatt MATH "The Appendix, written by J. Rogawski, explains the Jacquet-Langlands theory and indicates Deligne's proof of the Petersson-Ramanujan conjecture. It would merit its own review. (...) In conclusion, this is a wonderful way of transmitting recent mathematical research directly "from the producer to the consumer." - MathSciNet "The book is accessible to mature graduate students in mathematics and theoretical computer science. It is a nice presentation of a gem at the border of analysis, geometry, algebra and combinatorics. Those who take the effort to glance what happens behind the scene won't regret it." - Acta Scientiarum Mathematicarum

Synopsis:

Unifying concepts from various fields within mathematics, this volume offers solutions to two known problems - the construction of expanding graphs and the Ruziewicz problem, concerning the finitely additive invariant measures of spheres.

Table of Contents

0 Introduction. - 1 Expanding graphs. - 2 The Banach-Ruziewicz problem. - 3 Kazhdan Property (T) and its applications. - 4 The Laplacian and its eigenvalues. - 5 The representation theory of PGL2. - 6 Spectral decomposition of L2(G(Q)\G(A)). - 7 Banach-Ruziewicz problem for n = 2, 3; Ramanujan graphs. - 8 Some more discrete mathematics. - 9 Distributing points on the sphere. - 10 Open problems. - Appendix. - References. - Index.

Product Details

ISBN:
9783034603317
Author:
Lubotzky, Alex
Publisher:
Birkhauser
Author:
Lubotzky, Alexander
Author:
Rogawski, Jonathan D.
Location:
Basel
Subject:
Algebra - Abstract
Subject:
Mathematical Analysis
Subject:
Geometry - Differential
Subject:
Mathematics-Abstract Algebra
Subject:
Combinatorics
Subject:
Graph theory
Subject:
Kazhdan property
Subject:
Lie groups
Subject:
Measure theory
Subject:
Ramanujan conjecture
Subject:
Riemannian Geometry
Subject:
Ruziewicz problem
Subject:
Group Theory and Generalizations
Subject:
Real functions
Subject:
Number Theory
Subject:
Differential geometry
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Group Theory
Subject:
Global differential geometry.
Copyright:
Edition Description:
1st ed. 1994. 2nd printing
Series:
Modern Birkhäuser Classics
Publication Date:
20091131
Binding:
TRADE PAPER
Language:
English
Pages:
204
Dimensions:
235 x 155 mm 660 gr

Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » Group Theory

Discrete Groups, Expanding Graphs and Invariant Measures: Appendix by Jonathan D. Rogawski (Modern Birkhauser Classics) New Trade Paper
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Product details 204 pages Birkhauser Basel - English 9783034603317 Reviews:
"Synopsis" by , Unifying concepts from various fields within mathematics, this volume offers solutions to two known problems - the construction of expanding graphs and the Ruziewicz problem, concerning the finitely additive invariant measures of spheres.
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