Lubotzky, Alexander 1956
Overview
Works:  10 works in 71 publications in 5 languages and 1,586 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA178, 512.2 
Publication Timeline
.
Most widely held works by
Alexander Lubotzky
Discrete groups, expanding graphs and invariant measures
by
Alexander Lubotzky(
Book
)
26 editions published between 1994 and 2010 in English and French and held by 720 WorldCat member libraries worldwide
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, and the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres
26 editions published between 1994 and 2010 in English and French and held by 720 WorldCat member libraries worldwide
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, and the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres
Tree lattices
by
Hyman Bass(
Book
)
11 editions published between 2000 and 2001 in English and held by 318 WorldCat member libraries worldwide
Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a nonarchimedean local field acting on their BruhatTits trees. In particular this leads to a powerful method for studying lattices in such Lie groups. This monograph extends this approach to the more general investigation of Xlattices G, where Xis a locally finite tree and G is a discrete group of automorphisms of X of finite covolume. These "tree lattices" are the main object of study. Special attention is given to both parallels and contrasts with the case of Lie groups. Beyond the Lie group connection, the theory has application to combinatorics and number theory. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of nonuniform tree lattices, including some fundamental and recently proved existence theorems. Nonuniform tree lattices are much more complicated than uniform ones; thus a good deal of attention is given to the construction and study of diverse examples. The fundamental technique is the encoding of tree action in terms of the corresponding quotient "graphs of groups." Tree Lattices should be a helpful resource to researcher sin the field, and may also be used for a graduate course on geometric methods in group theory
11 editions published between 2000 and 2001 in English and held by 318 WorldCat member libraries worldwide
Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a nonarchimedean local field acting on their BruhatTits trees. In particular this leads to a powerful method for studying lattices in such Lie groups. This monograph extends this approach to the more general investigation of Xlattices G, where Xis a locally finite tree and G is a discrete group of automorphisms of X of finite covolume. These "tree lattices" are the main object of study. Special attention is given to both parallels and contrasts with the case of Lie groups. Beyond the Lie group connection, the theory has application to combinatorics and number theory. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of nonuniform tree lattices, including some fundamental and recently proved existence theorems. Nonuniform tree lattices are much more complicated than uniform ones; thus a good deal of attention is given to the construction and study of diverse examples. The fundamental technique is the encoding of tree action in terms of the corresponding quotient "graphs of groups." Tree Lattices should be a helpful resource to researcher sin the field, and may also be used for a graduate course on geometric methods in group theory
Subgroup growth
by
Alexander Lubotzky(
Book
)
12 editions published between 1993 and 2004 in English and held by 278 WorldCat member libraries worldwide
Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible "growth types", for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. For example the socalled PSG Theorem, proved in Chapter 5, characterizes the groups of polynomial subgroup growth as those which are virtually soluble of finite rank. A key element in the proof is the growth of congruence subgroups in arithmetic groups, a new kind of "noncommutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of noncommutative arithmetic arises with the introduction of subgroupcounting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite pgroups. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and strong approximation, algebraic and analytic number theory, probability, and padic model theory. Relevant aspects of such topics are explained in selfcontained "windows", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject
12 editions published between 1993 and 2004 in English and held by 278 WorldCat member libraries worldwide
Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible "growth types", for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. For example the socalled PSG Theorem, proved in Chapter 5, characterizes the groups of polynomial subgroup growth as those which are virtually soluble of finite rank. A key element in the proof is the growth of congruence subgroups in arithmetic groups, a new kind of "noncommutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of noncommutative arithmetic arises with the introduction of subgroupcounting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite pgroups. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and strong approximation, algebraic and analytic number theory, probability, and padic model theory. Relevant aspects of such topics are explained in selfcontained "windows", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject
Varieties of representations of finitely generated groups
by
Alexander Lubotzky(
Book
)
13 editions published in 1985 in English and Italian and held by 247 WorldCat member libraries worldwide
13 editions published in 1985 in English and Italian and held by 247 WorldCat member libraries worldwide
The word and riemannian metrics on lattices of semisimple groups
by
Alexander Lubotzky(
Book
)
3 editions published between 2000 and 2001 in English and held by 12 WorldCat member libraries worldwide
3 editions published between 2000 and 2001 in English and held by 12 WorldCat member libraries worldwide
Rekonstruktion und relative Chronologie : Akten der VIII. Fachtagung der Indogermanischen Gesellschaft, Leiden, 31. August4. September 1987
by Indogermanische Gesellschaft(
Book
)
2 editions published in 1992 in German and held by 6 WorldCat member libraries worldwide
2 editions published in 1992 in German and held by 6 WorldCat member libraries worldwide
Beauville surfaces and finite simple groups
by
Shelly Garion(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
A Beauville surface is a rigid complex surface of the form (C1 × C2)/G, where C1 and C2 are nonsingular, projective, higher genus curves, and G is a finite group acting freely on the product. Bauer, Catanese, and Grunewald conjectured that every finite simple group G, with the exception of A5, gives rise to such a surface. We prove that this is so for almost all finite simple groups (i.e., with at most finitely many exceptions). The proof makes use of the structure theory of finite simple groups, probability theory, and character estimates
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
A Beauville surface is a rigid complex surface of the form (C1 × C2)/G, where C1 and C2 are nonsingular, projective, higher genus curves, and G is a finite group acting freely on the product. Bauer, Catanese, and Grunewald conjectured that every finite simple group G, with the exception of A5, gives rise to such a surface. We prove that this is so for almost all finite simple groups (i.e., with at most finitely many exceptions). The proof makes use of the structure theory of finite simple groups, probability theory, and character estimates
The Eleventh Takagi lectures : 1718 November 2012, Tokyo
by Paul Frank Baum(
Book
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
Discrete groups, expanding graphs and invariant measures : preliminary version
by
Alexander Lubotzky(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Audience Level
0 

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Related Identities
 Bass, Hyman 1932 Author
 Segal, Daniel 1947
 Magid, Andy R. (Andy Roy) 1944
 Rogawski, Jonathan David Other Contributor
 Raghunathan, M. S.
 Mozes, Shahar
 Sarnak, Peter
 Lo, Wu
 Weitenberg, Jos Editor
 Beekes, Robert Stephen Paul Editor
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Associated Subjects
Algebra Algebraic varieties Combinatorial analysis Discrete groups Finite groups Geometry, Differential Global differential geometry Graph theory Group schemes (Mathematics) Group theory IndoEuropean languages Infinite groups Invariant measures Lfunctions Lie groups Mathematics Number theory Reconstruction (Linguistics) Representations of groups Subgroup growth (Mathematics) Topological groups Trees (Graph theory)