Valette, Alain
Overview
Works:  44 works in 124 publications in 3 languages and 2,658 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Honoree 
Classifications:  QA166, 511.5 
Publication Timeline
.
Most widely held works by
Alain Valette
Elementary number theory, group theory, and Ramanujan graphs
by
Giuliana P Davidoff(
)
16 editions published in 2003 in English and German and held by 1,405 WorldCat member libraries worldwide
This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering
16 editions published in 2003 in English and German and held by 1,405 WorldCat member libraries worldwide
This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering
Kazhdan's property (T)
by
M. Bachir Bekka(
Book
)
14 editions published in 2008 in English and held by 238 WorldCat member libraries worldwide
A comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics
14 editions published in 2008 in English and held by 238 WorldCat member libraries worldwide
A comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics
Introduction to the BaumConnes conjecture
by
Alain Valette(
Book
)
9 editions published in 2002 in English and held by 226 WorldCat member libraries worldwide
The BaumConnes conjecture is part of A. Connes' noncommutative geometry programme. It can be viewed as a conjectural generalisation of the AtiyahSinger index theorem, to the equivariant setting (the ambient manifold is not compact, but some compactness is restored by means of a proper, cocompact action of a group "gamma"). Like the AtiyahSinger theorem, the BaumConnes conjecture states that a purely topological object coincides with a purely analytical one. For a given group "gamma", the topological object is the equivariant Khomology of the classifying space for proper actions of "gamma", while the analytical object is the Ktheory of the C*algebra associated with "gamma" in its regular representation. The BaumConnes conjecture implies several other classical conjectures, ranging from differential topology to pure algebra. It has also strong connections with geometric group theory, as the proof of the conjecture for a given group "gamma" usually depends heavily on geometric properties of "gamma". This book is intended for graduate students and researchers in geometry (commutative or not), group theory, algebraic topology, harmonic analysis, and operator algebras. It presents, for the first time in book form, an introduction to the BaumConnes conjecture. It starts by defining carefully the objects in both sides of the conjecture, then the assembly map which connects them. Thereafter it illustrates the main tool to attack the conjecture (Kasparov's theory), and it concludes with a rough sketch of V. Lafforgue's proof of the conjecture for cocompact lattices in in Spn1, SL(3R), and SL(3C)
9 editions published in 2002 in English and held by 226 WorldCat member libraries worldwide
The BaumConnes conjecture is part of A. Connes' noncommutative geometry programme. It can be viewed as a conjectural generalisation of the AtiyahSinger index theorem, to the equivariant setting (the ambient manifold is not compact, but some compactness is restored by means of a proper, cocompact action of a group "gamma"). Like the AtiyahSinger theorem, the BaumConnes conjecture states that a purely topological object coincides with a purely analytical one. For a given group "gamma", the topological object is the equivariant Khomology of the classifying space for proper actions of "gamma", while the analytical object is the Ktheory of the C*algebra associated with "gamma" in its regular representation. The BaumConnes conjecture implies several other classical conjectures, ranging from differential topology to pure algebra. It has also strong connections with geometric group theory, as the proof of the conjecture for a given group "gamma" usually depends heavily on geometric properties of "gamma". This book is intended for graduate students and researchers in geometry (commutative or not), group theory, algebraic topology, harmonic analysis, and operator algebras. It presents, for the first time in book form, an introduction to the BaumConnes conjecture. It starts by defining carefully the objects in both sides of the conjecture, then the assembly map which connects them. Thereafter it illustrates the main tool to attack the conjecture (Kasparov's theory), and it concludes with a rough sketch of V. Lafforgue's proof of the conjecture for cocompact lattices in in Spn1, SL(3R), and SL(3C)
Proper group actions and the BaumConnes conjecture
by
Guido Mislin(
Book
)
8 editions published in 2003 in English and held by 206 WorldCat member libraries worldwide
This book contains a concise introduction to the techniques used to prove the BaumConnes conjecture. The BaumConnes conjecture predicts that the Khomology of the reduced C^*algebra of a group can be computed as the equivariant Khomology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological Khomology and the Ktheory of C^*algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to Khomology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature. The book is aimed at advanced graduate students and researchers in the area, leading to current research problems
8 editions published in 2003 in English and held by 206 WorldCat member libraries worldwide
This book contains a concise introduction to the techniques used to prove the BaumConnes conjecture. The BaumConnes conjecture predicts that the Khomology of the reduced C^*algebra of a group can be computed as the equivariant Khomology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological Khomology and the Ktheory of C^*algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to Khomology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature. The book is aimed at advanced graduate students and researchers in the area, leading to current research problems
Discrete groups and geometric structures : Workshop on Discrete Groups and Geometric Structures, with Applications III, May 2630, 2008, Kortrijk, Belgium
by *Workshop on *discrete *groups and *geometric structures(
Book
)
8 editions published in 2009 in English and held by 171 WorldCat member libraries worldwide
"This volume reports on research related to Discrete Groups and Geometric Structures, as presented during the International Workshop held May 2630, 2008, in Kortrijk, Belgium. Readers will benefit from impressive survey papers by John R. Parker on methods to construct and study lattices in complex hyperbolic space and by Ursula Hamenstädt on properties of group actions with a rankone element on proper CAT(0) spaces. This volume also contains research papers in the area of group actions and geometric structures, including work on loops on a twice punctured torus, the simplicial volume of products and fiber bundles, the homology of HantzscheWendt groups, rigidity of real Bott towers, circles in groups of smooth circle homeomorphisms, and groups generated by spine reflections admitting crooked fundamental domains."Publisher's website
8 editions published in 2009 in English and held by 171 WorldCat member libraries worldwide
"This volume reports on research related to Discrete Groups and Geometric Structures, as presented during the International Workshop held May 2630, 2008, in Kortrijk, Belgium. Readers will benefit from impressive survey papers by John R. Parker on methods to construct and study lattices in complex hyperbolic space and by Ursula Hamenstädt on properties of group actions with a rankone element on proper CAT(0) spaces. This volume also contains research papers in the area of group actions and geometric structures, including work on loops on a twice punctured torus, the simplicial volume of products and fiber bundles, the homology of HantzscheWendt groups, rigidity of real Bott towers, circles in groups of smooth circle homeomorphisms, and groups generated by spine reflections admitting crooked fundamental domains."Publisher's website
La propriété (T) de Kazhdan pour les groupes localement compacts
by
Pierre de La Harpe(
Book
)
11 editions published between 1988 and 1989 in French and held by 165 WorldCat member libraries worldwide
11 editions published between 1988 and 1989 in French and held by 165 WorldCat member libraries worldwide
Limits of graphs in group theory and computer science
(
Book
)
5 editions published in 2009 in English and held by 90 WorldCat member libraries worldwide
5 editions published in 2009 in English and held by 90 WorldCat member libraries worldwide
Le rôle des fibrés de rang fini en théorie de Kasparov équivariante
by
Alain Valette(
Book
)
7 editions published between 1987 and 1988 in French and held by 39 WorldCat member libraries worldwide
7 editions published between 1987 and 1988 in French and held by 39 WorldCat member libraries worldwide
Representation theory and complex analysis lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 1017, 2004
by
M Cowling(
)
4 editions published in 2008 in English and held by 33 WorldCat member libraries worldwide
4 editions published in 2008 in English and held by 33 WorldCat member libraries worldwide
Groups with the Haagerup property : Gromov's aTmenability
by
PierreAlain Cherix(
)
3 editions published in 2001 in English and held by 26 WorldCat member libraries worldwide
A locally compact group has the Haagerup property, or is aTmenable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space. As Gromov's pun is trying to indicate, this definition is designed as a strong negation to Kazhdan's property (T), characterized by the fact that every isometric action on some affine Hilbert space has a fixed point. The aim of this book is to cover, for the first time in book form, various aspects of the Haagerup property. New characterizations are brought in, using ergodic theory or operator algebras. Several new examples are given, and new approaches to previously known examples are proposed. Connected Lie groups with the Haagerup property are completely characterized
3 editions published in 2001 in English and held by 26 WorldCat member libraries worldwide
A locally compact group has the Haagerup property, or is aTmenable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space. As Gromov's pun is trying to indicate, this definition is designed as a strong negation to Kazhdan's property (T), characterized by the fact that every isometric action on some affine Hilbert space has a fixed point. The aim of this book is to cover, for the first time in book form, various aspects of the Haagerup property. New characterizations are brought in, using ergodic theory or operator algebras. Several new examples are given, and new approaches to previously known examples are proposed. Connected Lie groups with the Haagerup property are completely characterized
Industrialisation et développement : modèles, expériences, perspectives
(
Book
)
4 editions published in 1988 in French and Undetermined and held by 22 WorldCat member libraries worldwide
4 editions published in 1988 in French and Undetermined and held by 22 WorldCat member libraries worldwide
Les Méthodes de planification régionale au Cameroun
(
Book
)
1 edition published in 1971 in French and held by 3 WorldCat member libraries worldwide
1 edition published in 1971 in French and held by 3 WorldCat member libraries worldwide
Les Structures agraires au Brésil: Conséquences sur le développement économique du secteur agricole
by
Alain Valette(
Book
)
1 edition published in 1967 in French and held by 3 WorldCat member libraries worldwide
1 edition published in 1967 in French and held by 3 WorldCat member libraries worldwide
An elementary construction of Ramanujan graphs
by
Giuliana P Davidoff(
Book
)
2 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Discrete groups and geometric structures : Workshop on Discrete Groups and Geometric Structures, with Applications III, May 2008, Kortrijk, Belgium
(
Book
)
1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide
A quoi servent les mathématiques aujourd'hui?
by
Alain Valette(
)
1 edition published in 1990 in French and held by 2 WorldCat member libraries worldwide
1 edition published in 1990 in French and held by 2 WorldCat member libraries worldwide
SYNDROME DE LA TRAVERSEE THORACOBRACHIALE : ETUDE CLINIQUE ET THERAPEUTIQUE A PROPOS DE 18 OBSERVATIONS DE MALADES OPERES
by
Alain Valette(
Book
)
1 edition published in 1983 in French and held by 2 WorldCat member libraries worldwide
1 edition published in 1983 in French and held by 2 WorldCat member libraries worldwide
Spaces with measured walls, the Haagerup property and property (T)
by
PierreAlain Cherix(
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Discrete groups and geometric structures : 5th International Workshop on Discrete Groups and Geometric Structures, with Applications III, May 2008, K.U. Leuven Campus Kortrijk
by with Applications III International Workshop on Discrete Groups and Geometric Structures(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Kazhdan's Property (T). New Mathematical Monographs, Volume 11
(
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Property is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property: the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Property is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property: the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property
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Related Identities
 Sarnak, Peter
 Davidoff, Giuliana P. Author
 La Harpe, Pierre de Author
 Bekka, M. Bachir Author
 Mislin, Guido Author
 Dekimpe, Karel 1967 Editor
 Igodt, Paul 1956 Editor
 Burger, Marc
 Arzhantseva, Goulnara N. Editor
 Cowling, Michael Author
Associated Subjects
Algebra Algebraic topology BaumConnes conjecture Differential equations, Partial Discrete groups Fiber bundles (Mathematics) Geometrical constructions Geometry, Algebraic Graph theory Group theory Harmonic analysis Hilbert space KKtheory Ktheory Locally compact groups Mathematics Noncommutative differential geometry Number theory Operator algebras Quantum theory Representations of groups Topological groups