Groups and group theory

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied.

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings.

This volume presents the lecture notes from the authors' three summer courses offered during the program "e;Automorphisms of Free Groups: Geometry, Topology, and Dynamics,"e; held at the Centre de Recerca Matematica (CRM) in Bellaterra, Spain.

This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups.

This book contains selected papers based on talks given at the "e;Representation Theory, Number Theory, and Invariant Theory"e; conference held at Yale University from June 1 to June 5, 2015.

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space.

This textbook covers the general theory of Lie groups.

This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas.

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries.

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups.

This book explores generalized Lorenz-Mie theories when the illuminating beam is an electromagnetic arbitrary shaped beam relying on the method of separation of variables.

This book is the first one addressing quantum information from the viewpoint of group symmetry.

This book explains the group representation theory for quantum theory in the language of quantum theory.

This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids.

This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28.

This book contains a selection of papers presented at the session "e;Quaternionic and Clifford Analysis"e; at the 10th ISAAC Congress held in Macau in August 2015.

This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.

This book consists of both expository and research articles solicited from speakers at the conference entitled "e;Arithmetic and Ideal Theory of Rings and Semigroups,"e; held September 22-26, 2014 at the University of Graz, Graz, Austria.

This book features a selection of articles based on the XXXIV Bialowieza Workshop on Geometric Methods in Physics, 2015.

This monograph provides an accessible and comprehensive introduction to James Arthur's invariant trace formula, a crucial tool in the theory of automorphic representations.

Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014.

This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d'enfant.

Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups.

This text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto.

This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces.

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups.

The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhauser in 1981.

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.

Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist.

This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture.

This is a textbook that derives the fundamental theories of physics from symmetry.

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing.

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This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach.

This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators.

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces.

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites.

Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods.

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 "e;International Conference on Automorphic Forms and Number Theory,"e; held in Muscat, Sultanate of Oman.

We present an introduction to Berkovich's theory of non-archimedean analytic spaces that emphasizes its applications in various fields.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function.

In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems.

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory.

Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra.

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory.

Probability theory on compact Lie groups deals with the interaction between "e;chance"e; and "e;symmetry,"e; a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing).