Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry.

This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties.

This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems.

Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Bohning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov"

This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open questions and suggestions for further reading.

How can social bonds in society be strengthened? How do we learn and develop prosocial behaviour?
This comprehensive textbook provides up-to-date coverage of the social phenomenon of prosocial behaviour, incorporating all the major developments in the fields of developmental and social psychology. The first section identifies different forms of prosocial behaviour, including estimates of prevalence in everyday situations and the controversy between biological and cultural perspectives as explanatory models of prosocial behaviour. The second and third sections focus on learning and development, with emphasis on social learning, responsibility, empathy and guilt. The fourth section explores the prevalence of prosocial behaviour, in particular the situational and personality factors which inhibit urgently needed prosocial behaviour. The final section is devoted to practical applications, such as how to increase the likelihood that people will work as volunteers in community organisations and how to heighten the willingness to offer first aid.
This book will be an invaluable resource for both undergraduate and postgraduate students of social psychology and sociology, as well as anyone with an interest in social services and voluntary organisations.

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Social influence processes play a key role in human behavior. Arguably our extraordinary evolutionary success has much to do with our subtle and highly developed ability to interact with and influence each other. In this volume, leading international researchers review and integrate contemporary theory and research on the many ways people influence each other, considering both explicit, direct, and implicit, indirect influence strategies. Three sections examine fundamental processes and theory in social influence research, the role of cognitive processes and strategies in social influence phenomena, and the operation of social influence mechanisms in group settings. By applying the latest research to a wide range of interpersonal phenomena, this volume greatly advances our understanding of social influence mechanisms in strategic social interaction, and should be of interest to all students, researchers and practitioners interested in the dynamics of everyday interpersonal behavior.

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This book explores the role of listening in community engagement and peace building efforts, bridging academic research in communication and practical applications for individual and social change. For all their differences, community engagement and peacebuilding efforts share much in common: the need to establish and agree on achievable and measurable goals, the importance of trust, and the need for conflict management, to name but a few. This book presents listening-considered as a multi-disciplinary concept related to but distinct from civility, civic participation, and other social processes-as a primary mechanism for accomplishing these tasks. Individual chapters explore these themes in an array of international contexts, examining topics such as conflict resolution, restorative justice, environmental justice, migrants and refugees, and trauma-informed peacebuilding. The book includes contemporary literature reviews and theoretical insights covering the role of listening as related to individual, social, and governmental efforts to better engage communities and build, maintain, or establish peace in an increasingly divided world. This collection provides invaluable insight to researchers, students, educators, and practitioners in intercultural and international communication, conflict management, peacebuilding, community engagement, and international studies.

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next comes a thorough treatment of the theory of real hypersurfaces in complex space forms. A central focus is a complete proof of the classification of Hopf hypersurfaces with constant principal curvatures due to Kimura and Berndt. The book concludes with the basic theory of real hypersurfaces in quaternionic space forms, including statements of the major classification results and directions for further research.

Mathematical Methods in Practice Advisory Editors Bruno Brosowski UniversitAt Frankfurt Germany Gary F. Roach University of Strathclyde UK Volume 3 Applied Nonlinear Semigroups A. Belleni-Morante University of Florence, Italy A. C. McBride University of Strathclyde, UK In many disciplines such as physics, chemistry, biology, meteorology, electronics and economics, it is increasingly necessary to develop mathematical models that describe how the state of a system evolves with time. A useful way of studying such a model is to recast the appropriate evolution equation as an Abstract Cauchy Problem (ACP), which can then be analysed via the powerful theory of semigroups of operators. The user-friendly presentation in the book is centred on Abstract Cauchy Problems which model various processes such as particle transport, diffusion and combustion, all of which are examples of systems which evolve with time. The authors provide an introduction to the requisite concepts from functional analysis before moving on to the theory of semigroups of linear operators and their application to linear ACPs. These ideas are then applied to semilinear problems and fully nonlinear problems and it is shown how results from the linear theory can be extended. Finally, a variety of applications of practical interest are included. By leading a non-expert to the solutions of problems involving evolution equations via the theory of semigroups of operators, both linear and nonlinear, the book provides an accessible introduction to the treatment of the subject. The reader is assumed to have a basic knowledge of real analysis and vector spaces. M.Sc. and graduate students of functional analysis, applied mathematics, physics and engineering will find this an invaluable introduction to the subject.

Social influence processes play a key role in human behaviour. Arguably our extraordinary evolutionary success has much to do with our subtle and highly developed ability to interact with and influence each other. In this volume, leading international researchers review and integrate contemporary theory and research on the many ways people influence each other, considering both explicit, direct and implicit, indirect influence strategies. Three sections examine fundamental processes and theory in social influence research, the role of cognitive processes and strategies in social influence phenomena, and the operation of social influence mechanisms in group settings. By applying the latest research to a wide range of interpersonal phenomena, this volume greatly advances our understanding of social influence mechanisms in strategic social interaction, and will be valuable to all students, researchers and practitioners interested in the dynamics of everyday interpersonal behaviour.

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This book is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solutions without assuming the asymptotic setting. Next, this book addresses the quantum error correcting code with the symmetric structure of Weyl-Heisenberg groups. This structure leads to understand the quantum error correcting code systematically. Finally, this book focuses on the quantum universal information protocols by using the group SU(d). This topic can be regarded as a quantum version of the Csiszar-Korner's universal coding theory with the type method. The required mathematical knowledge about group representation is summarized in the companion book, Group Representation for Quantum Theory.

This innovative book examines radicalization from new psychological perspectives by examining the different typologies of radicalizing individuals, what makes individuals resilient against radicalization, and events that can trigger individuals to radicalize or to deradicalize. What is radicalization? Which psychological processes or events in a person's life play a role in radicalization? What determines whether a personal is resilient against radicalization, and is deradicalization something that we can achieve? This book goes beyond previous publications on this topic by identifying concrete key events in the process of radicalization, providing a useful theoretical framework that summarizes the current state-of-the-art research on radicalization and deradicalization. A model is presented in which a distinction is made between different levels of radicalization and deradicalization, with key underlying psychological needs discussed: the need for identity, justice, significance, and sensation. The authors also describe what makes people resilient against messages from "the outside world" when they belong to an extremist group and discuss observable events which may "trigger" a person to radicalize (further) or to deradicalize. Including real-world examples and clear guidelines for interventions aimed at prevention of radicalization and stimulation of deradicalization, this is essential reading for policy makers, researchers, practitioners, and students interested in this crucial societal issue.

Written by an algebraic topologist motivated by his own desire to learn, this book represents the compilation of results in the theory of polynomial invariants of finite groups. As well as covering invariant theory, the book also introduces some of the basic concepts behind ideal theory and homological algebra in a liberating context, and discusses the mutual impact of invariant theory and algebraic topology. Along the way, the author also examines such topics as the Hilbert-Noether finiteness theorems, methods for constructing invariants, the Poincare series, localization and use of gradings, and the Hilbert Syzygy theorem. Larry Smith includes numerous examples and illustrates the theorems by applying them to concrete cases.

Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.

Youth in Superdiverse Societies brings together theoretical, methodological and international approaches to the study of globalization, diversity, and acculturation in adolescence. It examines vital issues including migration, integration, cultural identities, ethnic minorities, and the interplay of ethnic and cultural diversity with experiences of growing up as an adolescent. This important volume focuses on understanding the experiences and consequences of multicultural societies and offers valuable new insights in the field of intergroup relations and the complexity of growingly heterogeneous societies. The book comprises four sections. The first includes fresh theoretical perspectives for studying youth development in multicultural societies, exploring topics such as superdiversity, globalization, bicultural identity development, polyculturalism, the interplay of acculturation and development, as well as developmental-ecological approaches. The second section highlights innovative methods in studying multicultural societies. It contains innovative dynamic concepts (e.g., experience-based sampling), methods for studying the nested structure of acculturative contexts, and suggestions for cross-comparative research to differentiate universal and context-specific processes. The third section examines social relations and social networks in diverse societies and features developmentally crucial contexts (e.g., family, peers, schools) and contributions on interethnic interactions in real-life contexts. The final section presents applications in natural settings and includes contributions on participatory action research and teachers dealings' with ethnic diversity. Each chapter provides a thorough overview of current research trends and findings, followed by detailed recommendations for future research, suggesting how the approaches can be cited, applied and improved. Youth in Superdiverse Societies is valuable reading for students studying adolescent acculturation and development in psychology, sociology, education, anthropology, linguistics and political science. It will also be of interest to scholars and researchers in social and developmental psychology, and related disciplines, as well as professionals in the field of migration.

This book offers a biographical account of Henri Tajfel, one of the most influential European social psychologists of the twentieth century, offering unique insights into his ground-breaking work in the areas of social perception, social identity and intergroup relations. The author, Rupert Brown, paints a vivid and personal portrait of Tajfel's life, his academic career and its significance to social psychology, and the key ideas he developed. It traces Tajfel's life from his birth in Poland just after the end of World War I, his time as a prisoner-of-war in World War II, his work with Jewish orphans and other displaced persons after that war, and thence to his short but glittering academic career as a social psychologist. Based on a range of sources including interviews, archival material, correspondence, photographs, and scholarly output, Brown expertly weaves together Tajfel's personal narrative with his evolving intellectual interests and major scientific discoveries. Following a chronological structure with each chapter dedicated to a significant transition period in Tajfel's life, the book ends with an appraisal of two of his principal posthumous legacies: the European Association of Social Psychology, a project always close to Tajfel's heart and for which he worked tirelessly; and the 'social identity approach' to social psychology initiated by Tajfel over forty years ago and now one of the discipline's most important perspectives. This is fascinating reading for students, established scholars, and anyone interested in social psychology and the life and lasting contribution of this celebrated scholar.

This book offers a biographical account of Henri Tajfel, one of the most influential European social psychologists of the twentieth century, offering unique insights into his ground-breaking work in the areas of social perception, social identity and intergroup relations. The author, Rupert Brown, paints a vivid and personal portrait of Tajfel's life, his academic career and its significance to social psychology, and the key ideas he developed. It traces Tajfel's life from his birth in Poland just after the end of World War I, his time as a prisoner-of-war in World War II, his work with Jewish orphans and other displaced persons after that war, and thence to his short but glittering academic career as a social psychologist. Based on a range of sources including interviews, archival material, correspondence, photographs, and scholarly output, Brown expertly weaves together Tajfel's personal narrative with his evolving intellectual interests and major scientific discoveries. Following a chronological structure with each chapter dedicated to a significant transition period in Tajfel's life, the book ends with an appraisal of two of his principal posthumous legacies: the European Association of Social Psychology, a project always close to Tajfel's heart and for which he worked tirelessly; and the 'social identity approach' to social psychology initiated by Tajfel over forty years ago and now one of the discipline's most important perspectives. This is fascinating reading for students, established scholars, and anyone interested in social psychology and the life and lasting contribution of this celebrated scholar.

This fascinating new book examines diversity in moral judgements, drawing on recent work in social, personality, and evolutionary psychology, reviewing the factors that influence the moral judgments people make. Why do reasonable people so often disagree when drawing distinctions between what is morally right and wrong? Even when individuals agree in their moral pronouncements, they may employ different standards, different comparative processes, or entirely disparate criteria in their judgments. Examining the sources of this variety, the author expertly explores morality using ethics position theory, alongside other theoretical perspectives in moral psychology, and shows how it can relate to contemporary social issues from abortion to premarital sex to human rights. Also featuring a chapter on applied contexts, using the theory of ethics positions to gain insights into the moral choices and actions of individuals, groups, and organizations in educational, research, political, medical, and business settings, the book offers answers that apply across individuals, communities, and cultures. Investigating the relationship between people's personal moral philosophies and their ethical thoughts, emotions, and actions, this is fascinating reading for students and academics from psychology and philosophy and anyone interested in morality and ethics.

This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.

In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

History, Trauma and Shame provides an in-depth examination of the sustained dialogue about the past between children of Holocaust survivors and descendants of families whose parents were either directly or indirectly involved in Nazi crimes. Taking an autobiographical narrative perspective, the chapters in the book explore the intersection of history, trauma and shame, and how change and transformation unfolds over time. The analyses of the encounters described in the book provides a close examination of the process of dialogue among members of The Study Group on Intergenerational Consequences of the Holocaust (PAKH), exploring how Holocaust trauma lives in the 'everyday' lives of descendants of survivors. It goes to the heart of the issues at the forefront of contemporary transnational debates about building relationships of trust and reconciliation in societies with a history of genocide and mass political violence. This book will be great interest for academics, researchers and postgraduate students engaged in the study of social psychology, Holocaust or genocide studies, cultural studies, reconciliation studies, historical trauma and peacebuilding. It will also appeal to clinical psychologists, psychiatrists and psychoanalysts, as well as upper-level undergraduate students interested in the above areas.

This volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12-17, 1993. The conference brought together specialists from all over the world who work in this field. All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection should point the way for further research. The volume should be of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics.

This is the fi rst textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of fi nite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the fi rst defi nitions up to Clifford theory, Brauer's induction theorem and the splitting fi eld theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet's result on primes in arithmetic progressions are given as an application. Examples of integral representations of fi nite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander- Buchsbaum theorem is proved. The Jordan-Zassenhaus theorem on the fi niteness of lattices in a given vector space is fully proved. Then the development and properties of class groups of orders is a fi rst focus. As a further highlight Swan's example of a stably free but not free ideal over the integral group ring of the generalised quaternion group of order 32 is developed in great detail. A student friendly introduction to ordinary representation theory Many examples and exercises, including solutions for some of them, make the book well suited for self-study Leads coherently from ordinary character theory to the integral representation theory of lattices over orders Several topics appear for the fi rst time in a textbook, such as Sin-Willems' approach to self-dual simple modules and Swan's example of a stably free non free ideal.

Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. * Provides physicists with a modern and accessible introduction to group theory* Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more* Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more* The essential textbook for students and an invaluable resource for researchers* Features a brief, self-contained treatment of linear algebra* An online illustration package is available to professors* Solutions manual (available only to professors)

--Core textbook featuring accessible but advanced coverage of theory, research, and applications in nonverbal communication from renowned scholars --Usable for undergraduate and graduate courses in communication and psychology departments --Includes a new chapter on identity and impression management, as well as fully updated research coverage throughout --Online resources include an extensive instructor's manual and test bank

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications. It also includes the most recent developments on other areas of mathematics including algebra and geometry. Lie group representation theory and harmonic analysis on Lie groups and on their homogeneous spaces form a significant and important area of mathematical research. These areas are interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics. Keeping up with the fast development of this exciting area of research, Ali Baklouti (University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars on the topic, the first of which took place on November 2009 in Kerkennah Islands, the second in Sousse on December 2011, and the third in Hammamet on December 2013. The last seminar, which took place December 18th to 23rd 2015 in Monastir, Tunisia, has promoted further research in all the fields where the main focus was in the area of Analysis, algebra and geometry and on topics of joint collaboration of many teams in several corners. Many experts from both countries have been involved.

This book features a selection of articles based on the XXXV Bialowieza Workshop on Geometric Methods in Physics, 2016. The series of Bialowieza workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Bialowieza Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.