Discrete Groups Expanding Graphs And Invariant Measures
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Discrete Groups Expanding Graphs And Invariant Measures
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Author : Alex Lubotzky
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-08-01
Discrete Groups Expanding Graphs And Invariant Measures written by Alex Lubotzky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-01 with Mathematics categories.
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.
Discrete Groups Expanding Graphs And Invariant Measures
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Author : Alexander Lubotzky
language : en
Publisher:
Release Date : 1989
Discrete Groups Expanding Graphs And Invariant Measures written by Alexander Lubotzky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Discrete Groups Expanding Graphs And Invariant Measures
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Author : Alex Lubotzky
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-17
Discrete Groups Expanding Graphs And Invariant Measures written by Alex Lubotzky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-17 with Mathematics categories.
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.
Discrete Groups Expanding Graphs And Invariant Measures
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Author : Alexander Lubotzky
language : fr
Publisher:
Release Date : 1994
Discrete Groups Expanding Graphs And Invariant Measures written by Alexander Lubotzky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Journal Of Fourier Analysis And Applications Special Issue
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Author : John J. Benedetto
language : en
Publisher: CRC Press
Release Date : 2020-03-10
Journal Of Fourier Analysis And Applications Special Issue written by John J. Benedetto and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.
The Journal of Fourier Analysis and Applications is a journal of the mathematical sciences devoted to Fourier analysis and its applications. The subject of Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences. At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. The large variety of topics discussed in this meeting, ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Jean-Pierre Kahane. Indeed, all of them are connected to his work. The mornings were devoted to plenary addresses while up to four parallel sessions took place in the afternoons. Altogether, there were about eighty speakers. This wide range of subjects appears in these proceedings which include thirty six articles.
Applying The Classification Of Finite Simple Groups
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Author : Stephen D. Smith
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-04-30
Applying The Classification Of Finite Simple Groups written by Stephen D. Smith and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-30 with Mathematics categories.
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Beauville Surfaces And Groups
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Author : Ingrid Bauer
language : en
Publisher: Springer
Release Date : 2015-04-14
Beauville Surfaces And Groups written by Ingrid Bauer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-14 with Mathematics categories.
This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces. It is the first time that these objects are discussed from the points of view of algebraic geometry as well as group theory. The book also includes various open problems and conjectures related to these surfaces. Beauville surfaces are a class of rigid regular surfaces of general type, which can be described in a purely algebraic combinatoric way. They play an important role in different fields of mathematics like algebraic geometry, group theory and number theory. The notion of Beauville surface was introduced by Fabrizio Catanese in 2000 and after the first systematic study of these surfaces by Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there has been an increasing interest in the subject. These proceedings reflect the topics of the lectures presented during the workshop ‘Beauville surfaces and groups 2012’, held at Newcastle University, UK in June 2012. This conference brought together, for the first time, experts of different fields of mathematics interested in Beauville surfaces.
Groups And Computation Ii
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Author : Larry Finkelstein, William M. Kantor
language : en
Publisher: American Mathematical Soc.
Release Date :
Groups And Computation Ii written by Larry Finkelstein, William M. Kantor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Algebra categories.
Consists of papers presented at the workshop on Groups and Computation held at DIMACS.
A Celebration Of The Mathematical Legacy Of Raoul Bott
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Author : Peter Robert Kotiuga
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-01-01
A Celebration Of The Mathematical Legacy Of Raoul Bott written by Peter Robert Kotiuga and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
Appalachian Set Theory
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Author : James Cummings
language : en
Publisher: Cambridge University Press
Release Date : 2012-11-15
Appalachian Set Theory written by James Cummings and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-15 with Mathematics categories.
Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.