Introduction To Approximate Groups

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Introduction To Approximate Groups

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Author : Matthew C. H. Tointon
language : en
Publisher: Cambridge University Press
Release Date : 2019-11-14

Introduction To Approximate Groups written by Matthew C. H. Tointon 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 2019-11-14 with Mathematics categories.

Provides a comprehensive exploration of the main concepts and techniques from the young, exciting field of approximate groups.

Thin Groups And Superstrong Approximation

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Author : Emmanuel Breuillard
language : en
Publisher: Cambridge University Press
Release Date : 2014-02-17

Thin Groups And Superstrong Approximation written by Emmanuel Breuillard 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 2014-02-17 with Mathematics categories.

This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.

Introduction To Sofic And Hyperlinear Groups And Connes Embedding Conjecture

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Author : Valerio Capraro
language : en
Publisher: Springer
Release Date : 2015-10-12

Introduction To Sofic And Hyperlinear Groups And Connes Embedding Conjecture written by Valerio Capraro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-12 with Mathematics categories.

This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.

Groups St Andrews 2013

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Author : C. M. Campbell
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-22

Groups St Andrews 2013 written by C. M. Campbell 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 2015-10-22 with Mathematics categories.

Leading researchers survey the latest developments in group theory and many related areas.

Compact Matrix Quantum Groups And Their Combinatorics

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Author : Amaury Freslon
language : en
Publisher: Cambridge University Press
Release Date : 2023-07-27

Compact Matrix Quantum Groups And Their Combinatorics written by Amaury Freslon 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 2023-07-27 with Mathematics categories.

An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.

Representations Of Finite Groups Of Lie Type

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Author : François Digne
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-05

Representations Of Finite Groups Of Lie Type written by François Digne 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 2020-03-05 with Mathematics categories.

An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.

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.

Cellular Automata And Groups

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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Springer Nature
Release Date : 2024-01-13

Cellular Automata And Groups written by Tullio Ceccherini-Silberstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-13 with Mathematics categories.

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.

Classical And Discrete Functional Analysis With Measure Theory

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Author : Martin Buntinas
language : en
Publisher: Cambridge University Press
Release Date : 2022-01-20

Classical And Discrete Functional Analysis With Measure Theory written by Martin Buntinas 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 2022-01-20 with Mathematics categories.

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

Introduction To The Functional Renormalization Group

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Author : Peter Kopietz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-03

Introduction To The Functional Renormalization Group written by Peter Kopietz 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 2010-05-03 with Language Arts & Disciplines categories.

This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.