Tullio Ceccherini-Silberstein's Books

Cellular Automata and Groups

By: Tullio Ceccherini-Silberstein,Michel Coornaert

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Cellular Automata and Groups

By: Tullio Ceccherini-Silberstein,Michel Coornaert

Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

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Page Count

446

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642140343

ISBN 13

9783642140341

Representation Theory of Finite Group Extensions

Clifford Theory, Mackey Obstruction, and the Orbit Method

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory of Finite Group Extensions

Clifford Theory, Mackey Obstruction, and the Orbit Method

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This monograph adopts an operational and functional analytic approach to the following problem: given a short exact sequence (group extension) 1 → N → G → H → 1 of finite groups, describe the irreducible representations of G by means of the structure of the group extension. This problem has attracted many mathematicians, including I. Schur, A.H. Clifford, and G. Mackey and, more recently, M. Isaacs, B. Huppert, Y.G. Berkovich & E.M. Zhmud, and J.M.G. Fell & R.S. Doran. The main topics are, on the one hand, Clifford Theory and the Little Group Method (of Mackey and Wigner) for induced representations, and, on the other hand, Kirillov’s Orbit Method (for step-2 nilpotent groups of odd order) which establishes a natural and powerful correspondence between Lie rings and nilpotent groups. As an application, a detailed description is given of the representation theory of the alternating groups, of metacyclic, quaternionic, dihedral groups, and of the (finite) Heisenberg group. The Little Group Method may be applied if and only if a suitable unitary 2-cocycle (the Mackey obstruction) is trivial. To overcome this obstacle, (unitary) projective representations are introduced and corresponding Mackey and Clifford theories are developed. The commutant of an induced representation and the relative Hecke algebra is also examined. Finally, there is a comprehensive exposition of the theory of projective representations for finite Abelian groups which is applied to obtain a complete description of the irreducible representations of finite metabelian groups of odd order.

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347

Publisher

Springer Nature

Published Date

ISBN 10

3031138732

ISBN 13

9783031138737

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.

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177

Publisher

Cambridge University Press

Published Date

ISBN 10

1107729912

ISBN 13

9781107729919

Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.

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589

Publisher

Cambridge University Press

Published Date

ISBN 10

1316863654

ISBN 13

9781316863657

Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.

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Page Count

153

Publisher

Springer Nature

Published Date

ISBN 10

3030516075

ISBN 13

9783030516079

Exercises in Cellular Automata and Groups

By: Tullio Ceccherini-Silberstein,Michel Coornaert

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Exercises in Cellular Automata and Groups

By: Tullio Ceccherini-Silberstein,Michel Coornaert

This book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk

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Page Count

638

Publisher

Springer Nature

Published Date

ISBN 10

3031103912

ISBN 13

9783031103919

Topics in Groups and Geometry

Growth, Amenability, and Random Walks

By: Tullio Ceccherini-Silberstein,Michele D'Adderio

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Topics in Groups and Geometry

Growth, Amenability, and Random Walks

By: Tullio Ceccherini-Silberstein,Michele D'Adderio

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

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Page Count

468

Publisher

Springer Nature

Published Date

ISBN 10

3030881091

ISBN 13

9783030881092

Representation Theory of the Symmetric Groups

The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory of the Symmetric Groups

The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood–Richardson rule and the Schur–Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.

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Page Count

429

Publisher

Cambridge University Press

Published Date

ISBN 10

113948396X

ISBN 13

9781139483964

Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Page Count

590

Publisher

Cambridge University Press

Published Date

ISBN 10

1316865401

ISBN 13

9781316865408

Cellular Automata and Groups

By: Tullio Ceccherini-Silberstein,Michel Coornaert

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Cellular Automata and Groups

By: Tullio Ceccherini-Silberstein,Michel Coornaert

This unique book provides a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric and combinatorial group theory, amenability, symbolic dynamics, the algebraic theory of group rings, and other branches of mathematics and theoretical computer science. The topics treated include the Garden of Eden theorem for amenable groups, the Gromov–Weiss surjunctivity theorem, and the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. Entirely self-contained and now in its second edition, the volume includes 10 appendices and more than 600 exercises, the solutions of which are presented in the companion book Exercises in Cellular Automata and Groups (2023) by the same authors. It will appeal to a large audience, including specialists and newcomers to the field.

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Page Count

562

Publisher

Springer Nature

Published Date

ISBN 10

3031433289

ISBN 13

9783031433283

Book's by Tullio Ceccherini-Silberstein

Cellular Automata and Groups

Cellular Automata and Groups

Representation Theory of Finite Group Extensions

Representation Theory of Finite Group Extensions

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Discrete Harmonic Analysis

Discrete Harmonic Analysis

Gelfand Triples and Their Hecke Algebras

Gelfand Triples and Their Hecke Algebras

Exercises in Cellular Automata and Groups

Exercises in Cellular Automata and Groups

Topics in Groups and Geometry

Topics in Groups and Geometry

Representation Theory of the Symmetric Groups

Representation Theory of the Symmetric Groups

Discrete Harmonic Analysis

Discrete Harmonic Analysis

Cellular Automata and Groups

Cellular Automata and Groups

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