Groups and group theory Books

Book SynopsisCommutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position oTrade Review'It gives a fresh picture of the subject for a new generation of students.' P. Scnezel, Zentralblatt fur Mathematik'The author takes care to explain the geometric and number theoretic meaning of the algebraic methods and results presented. This makes the book perhaps more demanding, but surely much more interesting than the standard ones.' European Mathematical Society Newsletter'Besides the usual topics … there are some welcome geometrical illustrations, as well as some homespun philosophy.' MathematicaTable of ContentsHello!; 1. Basics; 2. Modules; 3. Noetherian rings; 4. Finite extensions and Noether normalisation; 5. The nullstellensatz and spec A; 6. Rings of fractions S-1A and localisation; 7. Primary decomposition; 8. DVRs and normal integral domains; 9. Goodbye!; Bibliography.

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Book SynopsisCommutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position oTrade Review'It gives a fresh picture of the subject for a new generation of students.' P. Scnezel, Zentralblatt fur Mathematik'The author takes care to explain the geometric and number theoretic meaning of the algebraic methods and results presented. This makes the book perhaps more demanding, but surely much more interesting than the standard ones.' European Mathematical Society Newsletter'Besides the usual topics … there are some welcome geometrical illustrations, as well as some homespun philosophy.' MathematicaTable of ContentsHello!; 1. Basics; 2. Modules; 3. Noetherian rings; 4. Finite extensions and Noether normalisation; 5. The nullstellensatz and spec A; 6. Rings of fractions S-1A and localisation; 7. Primary decomposition; 8. DVRs and normal integral domains; 9. Goodbye!; Bibliography.

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Book SynopsisThis text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering.Trade Review'The book under review is an attractively written excellent text which successfully bridges the gap between undergraduate instruction and current research. Hence it is very well suited to bring a fresh breeze into the classroom. The reviewer warmly recommends this text to any lecturer looking for an attractive theme and to everybody else for great supplementary reading. Of course, this book should not be missed in any institutional library.' Zentralblatt MATH'A light touch and the inclusion of some unexpected results make the book a pleasure to read.' MathematikaTable of ContentsAn overview; 1. Graph theory; 2. Number theory; 3. PSL2(q); 4. The graphs Xp,q; Appendix A. 4-regular graphs with large girth; Index; Bibliography.

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Book SynopsisL-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.Trade Review'… a gentle introduction to this fascinating new subject. The presentation is very explicit and many examples are worked out with great detail … This book should be of great interest to students beginning with the theory of modular forms or for more advanced readers wanting to know about general L-functions.' Emmanuel P. Royer, Mathematical Reviews'This book, whose clear and sometimes simplified proofs make the basic theory of automorphic forms on GL(n) accessible to a wide audience, will be valuable for students. It nicely complements D. Bump's book (Automorphic Forms and Representations, Cambridge, 1997), which offers a greater emphasis on representation theory and a different selection of topics.' Zentralblatt MATH'Unfortunately, when n > 2 the GL(n) theory is not very accessible to the student of analytic number theory, yet it is increasing in importance. [This book] addresses this problem by developing a large part of the theory in a way that is carefully designed to make the field accessible … much of the literature is written in the adele language, and seeing how it translates into classical terms is both useful and enlightening … This is a unique and very welcome book, one that the student of automorphic forms will want to study, and also useful to experts.' Daniel Bump, SIAM ReviewTable of ContentsIntroduction; 1. Discrete group actions; 2. Invariant differential operators; 3. Automorphic forms and L-functions for SL(2,Z); 4. Existence of Maass forms; 5. Maass forms and Whittaker functions for SL(n,Z); 6. Automorphic forms and L-functions for SL(3,Z); 7. The Gelbert–Jacquet lift; 8. Bounds for L-functions and Siegel zeros; 9. The Godement–Jacquet L-function; 10. Langlands Eisenstein series; 11. Poincaré series and Kloosterman sums; 12. Rankin–Selberg convolutions; 13. Langlands conjectures; Appendix. The GL(n)pack manual; References.

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Book SynopsisThe Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, and has now expanded into such areas as Geometry and Quantum Field Theory, tying together seemingly unrelated disciplines into a web of tantalizing conjectures. A new chapter to this grand project is provided in this book. It develops the geometric Langlands Correspondence for Loop Groups, a new approach, from a unique perspective offered by affine Kac-Moody algebras. The theory offers fresh insights into the world of Langlands dualities, with many applications to Representation Theory of Infinite-dimensional Algebras, and Quantum Field Theory. This accessible text builds the theory from scratch, with all necessary concepts defined and the essential results proved along the way. Based on courses taught at Berkeley, the book provides many open problems which could form the basis for future research, and is accessible to advanced undergraduate students and beginning graduate sTrade Review'This book is well written and will give especially the interested student, an excellent basis in this rapidly developing area of mathematics. For those beyond the level of student it also provides very useful text to follow, and perhaps to participate, in these developments.' Samuel James Patterson, Zentralblatt MATHTable of ContentsPreface; 1. Local Langlands Correspondence; 2. Vertex algebras; 3. Constructing central elements; 4. Opers and the center for a general Lie algebra; 5. Free field realization; 6. Wakimoto modules; 7. Intertwining operators; 8. Identification of the center with functions on opers; 9. Structure of bg-modules of critical level; 10. Constructing the local Langlands Correspondence; Appendix; References.

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Book SynopsisDevelops a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. This book formulates simple general conditions on the spectral theory of the group and the regularity of the averaging sets, which suffice to guarantee convergence to the ergodic mean.Table of ContentsPreface vii 0.1 Main objectives vii 0.2 Ergodic theory and amenable groups viii 0.3 Ergodic theory and nonamenable groups x Chapter 1. Main results: Semisimple Lie groups case 1 1.1 Admissible sets 1 1.2 Ergodic theorems on semisimple Lie groups 2 1.3 The lattice point-counting problem in admissible domains 4 1.4 Ergodic theorems for lattice subgroups 6 1.5 Scope of the method 8 Chapter 2. Examples and applications 11 2.1 Hyperbolic lattice points problem 11 2.2 Counting integral unimodular matrices 12 2.3 Integral equivalence of general forms 13 2.4 Lattice points in S-algebraic groups 15 2.5 Examples of ergodic theorems for lattice actions 16 Chapter 3. Definitions, preliminaries, and basic tools 19 3.1 Maximal and exponential-maximal inequalities 19 3.2 S-algebraic groups and upper local dimension 21 3.3 Admissible and coarsely admissible sets 21 3.4 Absolute continuity and examples of admissible averages 23 3.5 Balanced and well-balanced families on product groups 26 3.6 Roughly radial and quasi-uniform sets 27 3.7 Spectral gap and strong spectral gap 29 3.8 Finite-dimensional subrepresentations 30 Chapter 4. Main results and an overview of the proofs 33 4.1 Statement of ergodic theorems for S-algebraic groups 33 4.2 Ergodic theorems in the absence of a spectral gap: overview 35 4.3 Ergodic theorems in the presence of a spectral gap: overview 38 4.4 Statement of ergodic theorems for lattice subgroups 40 4.5 Ergodic theorems for lattice subgroups: overview 42 4.6 Volume regularity and volume asymptotics: overview 44 Chapter 5. Proof of ergodic theorems for S-algebraic groups 47 5.1 Iwasawa groups and spectral estimates 47 5.2 Ergodic theorems in the presence of a spectral gap 50 5.3 Ergodic theorems in the absence of a spectral gap, I 56 5.4 Ergodic theorems in the absence of a spectral gap, II 57 5.5 Ergodic theorems in the absence of a spectral gap, III 60 5.6 The invariance principle and stability of admissible averages 67 Chapter 6. Proof of ergodic theorems for lattice subgroups 71 6.1 Induced action 71 6.2 Reduction theorems 74 6.3 Strong maximal inequality 75 6.4 Mean ergodic theorem 78 6.5 Pointwise ergodic theorem 83 6.6 Exponential mean ergodic theorem 84 6.7 Exponential strong maximal inequality 87 6.8 Completion of the proofs 90 6.9 Equidistribution in isometric actions 91 Chapter 7. Volume estimates and volume regularity 93 7.1 Admissibility of standard averages 93 7.2 Convolution arguments 98 7.3 Admissible, well-balanced, and boundary-regular families 101 7.4 Admissible sets on principal homogeneous spaces 105 7.5 Tauberian arguments and Holder continuity 107 Chapter 8. Comments and complements 113 8.1 Lattice point-counting with explicit error term 113 8.2 Exponentially fast convergence versus equidistribution 115 8.3 Remark about balanced sets 116 Bibliography 117 Index 121

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Book SynopsisExplores an important aspect of number theory - the theory of exponential sums over finite fields and their Mellin transforms - from a categorical point of view. This book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.Trade Review"The book is written in a clear and enlightening style. The author provides the reader with many examples that are developed throughout a dozen chapters. These examples help understand and clarify the depth and the variety of applications of the beautiful main equidistribution statement that relies on rather complicated and subtle algebrageometric arguments."--Florent Jouve, Mathematical Reviews Clippings "The book provides the reader with much material around the question of the equidistribution of the angles if one fixes f and varies over the multiplicative character x. More than one hundred pages of examples provide the reader with great insight in the different applications of the main theorem. This turns the book into a very good basis for research in this area."--Manfred G. Madritsch, Zentralblatt MATH "Once a certain basic understanding is reached, this book, like the others written by N. Katz, reveals itself to be very precisely and sharply written, and to be full of riches. And finally, this theory shows spectacularly how some of the most abstract ideas of algebra and algebraic geometry may be essential to solving extremely concrete problems."--Emmanuel Kowalski, Bulletin of the American Mathematical SocietyTable of Contents*FrontMatter, pg. i*Contents, pg. vi*Introduction, pg. 1*CHAPTER 1. Overview, pg. 7*CHAPTER 2. Convolution of Perverse Sheaves, pg. 19*CHAPTER 3. Fibre Functors, pg. 21*CHAPTER 4. The Situation over a Finite Field, pg. 25*CHAPTER 5. Frobenius Conjugacy Classes, pg. 31*CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith, pg. 33*CHAPTER 7. The Main Theorem, pg. 39*CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility, pg. 45*CHAPTER 9. Autodualities and Signs, pg. 49*CHAPTER 10. A First Construction of Autodual Objects, pg. 53*CHAPTER 11. A Second Construction of Autodual Objects, pg. 55*CHAPTER 12. The Previous Construction in the Nonsplit Case, pg. 61*CHAPTER 13. Results of Goursat-Kolchin-Ribet Type, pg. 63*CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick, pg. 67*CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family, pg. 73*CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith, pg. 77*CHAPTER 17. GL(n) Examples, pg. 81*CHAPTER 18. Symplectic Examples, pg. 89*CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples, pg. 103*CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples, pg. 113*CHAPTER 21. SL(n) Examples, for n an Odd Prime, pg. 125*CHAPTER 22. SL(n) Examples with Slightly Composite n, pg. 135*CHAPTER 23. Other SL(n) Examples, pg. 141*CHAPTER 24. An O(2n) Example, pg. 145*CHAPTER 25. G2 Examples: the Overall Strategy, pg. 147*CHAPTER 26. G2 Examples: Construction in Characteristic Two, pg. 155*CHAPTER 27. G2 Examples: Construction in Odd Characteristic, pg. 163*CHAPTER 28. The Situation over Z: Results, pg. 173*CHAPTER 29. The Situation over Z: Questions, pg. 181*CHAPTER 30. Appendix: Deligne's Fibre Functor, pg. 187*Bibliography, pg. 193*Index, pg. 197

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Book SynopsisConsiders the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. This book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension.Trade Review"Zannier's book is well written and a pleasure to read... [T]he author always makes an effort to point out key ideas and key steps, so a reader who wants to read and understand the complete proofs in this technically demanding field will find this monograph to be an extremely helpful entree into the subject... [T]he reviewer highly recommends Zannier's book as an excellent survey of and introduction to the important and hot topic of unlikely intersections in arithmetic geometry."--Joseph H. Silverman, Bulletin of the AMS "This book is indeed a great source of knowledge and inspiration for everybody interested in the unlikely intersection problems. The author must be commended for doing this job, and doing it so well."--Yuri Bilu, Mathematical Reviews ClippingsTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. ix*Notation and Conventions, pg. xi*Introduction: An Overview of Some Problems of Unlikely Intersections, pg. 1*Chapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture, pg. 15*Chapter 2: An Arithmetical Analogue, pg. 43*Chapter 3 Unlikely Intersections in Elliptic Surfaces and Problems of Masser, pg. 62*Chapter 4: About the Andre-Oort Conjecture, pg. 96*Appendix A: Distribution of Rational Points on Subanalytic Surfaces, pg. 128*Appendix B: Uniformity in Unlikely Intersections: An Example for Lines in Three Dimensions, pg. 136*Appendix C: Silverman's Bounded Height Theorem for Elliptic Curves: A Direct Proof, pg. 138*Appendix D: Lower Bounds for Degrees of Torsion Points: The Transcendence Approach, pg. 140*Appendix E: A Transcendence Measure for a Quotient of Periods, pg. 143*Appendix F: Counting Rational Points on Analytic Curves: A Transcendence Approach, pg. 145*Appendix G: Mixed Problems: Another Approach, pg. 147*Bibliography, pg. 149*Index, pg. 159

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Book SynopsisMumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book provides a comprehensive exploration of Mumford-Tate groups and domains.Trade Review"The brilliance of the results and their broad spectrum of their applications makes this book an outstanding piece. Yet, there is more to write and to develop: the authors suggest the existence of future lines of research for a next book."--Jonathan Sanchez Hernandez, European Mathematical SocietyTable of ContentsIntroduction 1 I Mumford-Tate Groups 28 I.A Hodge structures 28 I.B Mumford-Tate groups 32 I.C Mixed Hodge structures and their Mumford-Tate groups 38 II Period Domains and Mumford-Tate Domains 45 II.A Period domains and their compact duals 45 II.B Mumford-Tate domains and their compact duals 55 II.C Noether-Lefschetz loci in period domains 61 III The Mumford-Tate Group of a Variation of Hodge Structure 67 III.A The structure theorem for variations of Hodge structures 69 III.B An application of Mumford-Tate groups 78 III.C Noether-Lefschetz loci and variations of Hodge structure .81 IV Hodge Representations and Hodge Domains 85 IV.A Part I: Hodge representations 86 IV.B The adjoint representation and characterization of which weights give faithful Hodge representations 109 IV.C Examples: The classical groups 117 IV.D Examples: The exceptional groups 126 IV.E Characterization of Mumford-Tate groups 132 IV.F Hodge domains 149 IV.G Mumford-Tate domains as particular homogeneous complex manifolds 168 Appendix: Notation from the structure theory of semisimple Lie algebras 179 V Hodge Structures with Complex Multiplication 187 V.A Oriented number fields 189 V.B Hodge structures with special endomorphisms 193 V.C A categorical equivalence 196 V.D Polarization and Mumford-Tate groups . 198 V.E An extended example 202 V.F Proofs of Propositions V.D.4 and V.D.5 in the Galois case 209 VI Arithmetic Aspects of Mumford-Tate Domains 213 VI.A Groups stabilizing subsets of D 215 VI.B Decomposition of Noether-Lefschetz into Hodge orientations 219 VI.C Weyl groups and permutations of Hodge orientations 231 VI.D Galois groups and fields of definition 234 Appendix: CM points in unitary Mumford-Tate domains 239 VII Classification of Mumford-Tate Subdomains 240 VII.A A general algorithm 240 VII.B Classification of some CM-Hodge structures 243 VII.C Determination of sub-Hodge-Lie-algebras 246 VII.D Existence of domains of type IV(f) 251 VII.E Characterization of domains of type IV(a) and IV(f) 253 VII.F Completion of the classification for weight 3 256 VII.G The weight 1 case 260 VII.H Algebro-geometric examples for the Noether-Lefschetzlocus types 265 VIII Arithmetic of Period Maps of Geometric Origin 269 VIII.A Behavior of fields of definition under the period Map -- image and preimage 270 VIII.B Existence and density of CM points in motivic VHS 275 Bibliography 277 Index 287

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Book SynopsisMumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book provides a comprehensive exploration of Mumford-Tate groups and domains.Trade Review"The brilliance of the results and their broad spectrum of their applications makes this book an outstanding piece. Yet, there is more to write and to develop: the authors suggest the existence of future lines of research for a next book."--Jonathan Sanchez Hernandez, European Mathematical SocietyTable of ContentsIntroduction 1 I Mumford-Tate Groups 28 I.A Hodge structures 28 I.B Mumford-Tate groups 32 I.C Mixed Hodge structures and their Mumford-Tate groups 38 II Period Domains and Mumford-Tate Domains 45 II.A Period domains and their compact duals 45 II.B Mumford-Tate domains and their compact duals 55 II.C Noether-Lefschetz loci in period domains 61 III The Mumford-Tate Group of a Variation of Hodge Structure 67 III.A The structure theorem for variations of Hodge structures 69 III.B An application of Mumford-Tate groups 78 III.C Noether-Lefschetz loci and variations of Hodge structure .81 IV Hodge Representations and Hodge Domains 85 IV.A Part I: Hodge representations 86 IV.B The adjoint representation and characterization of which weights give faithful Hodge representations 109 IV.C Examples: The classical groups 117 IV.D Examples: The exceptional groups 126 IV.E Characterization of Mumford-Tate groups 132 IV.F Hodge domains 149 IV.G Mumford-Tate domains as particular homogeneous complex manifolds 168 Appendix: Notation from the structure theory of semisimple Lie algebras 179 V Hodge Structures with Complex Multiplication 187 V.A Oriented number fields 189 V.B Hodge structures with special endomorphisms 193 V.C A categorical equivalence 196 V.D Polarization and Mumford-Tate groups . 198 V.E An extended example 202 V.F Proofs of Propositions V.D.4 and V.D.5 in the Galois case 209 VI Arithmetic Aspects of Mumford-Tate Domains 213 VI.A Groups stabilizing subsets of D 215 VI.B Decomposition of Noether-Lefschetz into Hodge orientations 219 VI.C Weyl groups and permutations of Hodge orientations 231 VI.D Galois groups and fields of definition 234 Appendix: CM points in unitary Mumford-Tate domains 239 VII Classification of Mumford-Tate Subdomains 240 VII.A A general algorithm 240 VII.B Classification of some CM-Hodge structures 243 VII.C Determination of sub-Hodge-Lie-algebras 246 VII.D Existence of domains of type IV(f) 251 VII.E Characterization of domains of type IV(a) and IV(f) 253 VII.F Completion of the classification for weight 3 256 VII.G The weight 1 case 260 VII.H Algebro-geometric examples for the Noether-Lefschetzlocus types 265 VIII Arithmetic of Period Maps of Geometric Origin 269 VIII.A Behavior of fields of definition under the period Map -- image and preimage 270 VIII.B Existence and density of CM points in motivic VHS 275 Bibliography 277 Index 287

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Book SynopsisProvides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. This title delves into arguments originating in Nori's work that have been further developed by others.Trade Review"This dense, fascinating book by Voisin is a report of some of the exciting discoveries she has made in the quest of the secrets of algebraic cycles."--Alberto Collino, Zentralblatt MATH "[An advanced] reader will find a rich collection of ideas as well as detailed machinery with which to attack difficult problems in the field. Any complex geometer interested in the interplay between algebraic cycles, Hodge theory and algebraic topology should have this book on his or her shelf."--C. A. M. Peters, Mathematical Reviews ClippingsTable of ContentsPreface vii 1Introduction 1 1.1 Decomposition of the diagonal and spread 3 1.2 The generalized Bloch conjecture 7 1.3 Decomposition of the small diagonal and application to the topology of families 9 1.4 Integral coefficients and birational invariants 11 1.5 Organization of the text 13 2Review of Hodge theory and algebraic cycles 15 2.1 Chow groups 15 2.2 Hodge structures 24 3Decomposition of the diagonal 36 3.1 A general principle 36 3.2 Varieties with small Chow groups 44 4Chow groups of large coniveau complete intersections 55 4.1 Hodge coniveau of complete intersections 55 4.2 Coniveau 2 complete intersections 64 4.3 Equivalence of generalized Bloch and Hodge conjectures for general complete intersections 67 4.4 Further applications to the Bloch conjecture on 0-cycles on surfaces 86 5On the Chow ring of K3 surfaces and hyper-Kahler manifolds 88 5.1 Tautological ring of a K3 surface 88 5.2 A decomposition of the small diagonal 96 5.3 Deligne's decomposition theorem for families of K3 surfaces 106 6Integral coefficients 123 6.1 Integral Hodge classes and birational invariants 123 6.2 Rationally connected varieties and the rationality problem 127 6.3 Integral decomposition of the diagonal and the structure of the Abel-Jacobi map 139 Bibliography 155 Index 163

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Book SynopsisProvides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. This title delves into arguments originating in Nori's work that have been further developed by others.Trade Review"This dense, fascinating book by Voisin is a report of some of the exciting discoveries she has made in the quest of the secrets of algebraic cycles."--Alberto Collino, Zentralblatt MATH "[An advanced] reader will find a rich collection of ideas as well as detailed machinery with which to attack difficult problems in the field. Any complex geometer interested in the interplay between algebraic cycles, Hodge theory and algebraic topology should have this book on his or her shelf."--C. A. M. Peters, Mathematical Reviews ClippingsTable of ContentsPreface vii 1Introduction 1 1.1 Decomposition of the diagonal and spread 3 1.2 The generalized Bloch conjecture 7 1.3 Decomposition of the small diagonal and application to the topology of families 9 1.4 Integral coefficients and birational invariants 11 1.5 Organization of the text 13 2Review of Hodge theory and algebraic cycles 15 2.1 Chow groups 15 2.2 Hodge structures 24 3Decomposition of the diagonal 36 3.1 A general principle 36 3.2 Varieties with small Chow groups 44 4Chow groups of large coniveau complete intersections 55 4.1 Hodge coniveau of complete intersections 55 4.2 Coniveau 2 complete intersections 64 4.3 Equivalence of generalized Bloch and Hodge conjectures for general complete intersections 67 4.4 Further applications to the Bloch conjecture on 0-cycles on surfaces 86 5On the Chow ring of K3 surfaces and hyper-Kahler manifolds 88 5.1 Tautological ring of a K3 surface 88 5.2 A decomposition of the small diagonal 96 5.3 Deligne's decomposition theorem for families of K3 surfaces 106 6Integral coefficients 123 6.1 Integral Hodge classes and birational invariants 123 6.2 Rationally connected varieties and the rationality problem 127 6.3 Integral decomposition of the diagonal and the structure of the Abel-Jacobi map 139 Bibliography 155 Index 163

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Book SynopsisProvides an introduction to Hodge theory - one of the central and most vibrant areas of contemporary mathematics - from leading specialists on the subject. This book includes topics that range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps.Trade Review"Charles and Schnell's chapter beautifully surveys the theory of absolute Hodge classes, giving in particular a complete proof of Deligne's theorem on absolute Hodge classes on abelian varieties... A welcome addition to the literature and should be useful to both graduate students and researchers working in Hodge theory."--Dan Petersen, MathSciNetTable of Contents*FrontMatter, pg. i*Contributors, pg. v*Contents, pg. vii*Preface, pg. xv*Chapter One. Introduction to Kahler Manifolds, pg. 1*Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem, pg. 70*Chapter Three. Mixed Hodge Structures, pg. 123*Chapter Four. Period Domains and Period Mappings, pg. 217*Chapter Five. The Hodge Theory of Maps, pg. 257*Chapter Six The Hodge Theory of Maps, pg. 273*Chapter Seven. Introduction to Variations of Hodge Structure, pg. 297*Chapter Eight. Variations of Mixed Hodge Structure, pg. 333*Chapter Nine. Lectures on Algebraic Cycles and Chow Groups, pg. 410*Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles, pg. 449*Chapter Eleven. Notes on Absolute Hodge Classes, pg. 469*Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective, pg. 531*Bibliography, pg. 574*Index, pg. 577

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Book SynopsisTrade Review"The authors give a very detailed introduction to the theory, smoothing out some difficulties by introducing new concepts."--Gerd Faltings, Zentralblatt MATHTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. ix*Chapter I. Representations of the fundamental group and the torsor of deformations. An overview, pg. 1*Chapter II. Representations of the fundamental group and the torsor of deformations. Local study, pg. 27*Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects, pg. 179*Chapter IV. Cohomology of Higgs isocrystals, pg. 307*Chapter V. Almost etale coverings, pg. 449*Chapter VI. Covanishing topos and generalizations, pg. 485*Facsimile : A p-adic Simpson correspondence, pg. 577*Bibliography, pg. 595*Indexes, pg. 599

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Book SynopsisFeaturing strategies for solving the puzzles and computations illustrated using the SAGE open-source computer algebra system, the second edition of Adventures in Group Theory is perfect for mathematics enthusiasts and for use as a supplementary textbook.Trade Review"Adventures in Group Theory is a tour through the algebra of several 'permutation puzzles'... If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book." - MAA Online "Joyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts." - Choice "Joyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik's Cube. Enthusiastic students will learn a lot of mathematics from this book." - American Scientist"Table of ContentsPrefaceAcknowledgmentsWhere to Begin...1. Elementary, my dear Watson2. 'And you do addition?'3. Bell ringing and other permutations4. A procession of permutation puzzles5. What's commutative and purple?6. Welcome to the machine7. 'God's algorithm' and graphs8. Symmetry and the Platonic solids9. The illegal cube group10. Words which move11. The (legal) Rubik's Cube group12. Squares, two-faces, and other subgroups13. Other Rubik-like puzzle groups14. Crossing the Rubicon15. Some solution strategies16. Coda: Questions and other directionsBibliographyIndex

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Book SynopsisThe second of two volumes addressing theoretical problems associated with consensual action of task-orientated small groups. Less formal than the first volume, this work tends to be more general in approach focusing on interpersonal relations and social processes within such groups.Trade Review"The field has long been preoccupied by certain topics--decision making, leadership, and performance--and the contents reflect that continuing emphasis. Witte and Davis have done the field a great service in bringing these papers together for publication."—Contemporary PsychologyTable of ContentsVolume 1.Contents: Preface. Part I: Introduction.J.H. Davis, Small-Group Research and the Steiner Questions: The Once and Future Thing. Part II: Social Aggregation and Combination Models.H.W. Crott, J. Werner, C. Hoffmann, A Probabilistic Model of Opinion Change Considering Distance Between Alternatives: An Application to Mock Jury Data. J.H. Davis, Group Decision Making and Quantitative Judgments: A Consensus Model. P.R. Laughlin, Group Decision Making and Collective Induction. R.S. Tindale, C.M. Smith, L.S. Thomas, J. Filkins, S. Sheffey, Shared Representations and Asymmetric Social Influence Processes in Small Groups. N.L. Kerr, R.J. MacCoun, G.P. Kramer, "When are N Heads Better (or Worse) Than One?": Biased Judgment in Individuals Versus Groups. T. Kameda, Procedural Influence in Consensus Formation: Evaluating Group Decision Making From a Social Choice Perspective. Part III: Social Information-Processing Models.G. Stasser, S.I. Vaughan, Models of Participation During Fact-to-Face Unstructured Discussion. B. Latané, Strength From Weakness: The Fate of Opinion Minorities in Spatially Distributed Groups. D. Gigone, R. Hastie, The Impact of Information on Group Judgment: A Model and Computer Simulation. E.H. Witte, The Extended Group Situation Theory (EGST): Explaining the Amount of Change. S. Galam, When Humans Interact Like Atoms. J.H. Davis, Concluding Remarks. Volume 2.Contents: Preface. Part I: Introduction.E.H. Witte, Small-Group Research and the Crisis of Social Psychology: An Introduction. Part IIGroup Structure and Composition.R.L. Moreland, J.M. Levine, M.L. Weingert, Creating the Ideal Group: Composition Effects at Work. W. Stroebe, M. Diehl, G. Abakoumkin, Social Compensation and the Köhler Effect: Toward a Theoretical Explanation of Motivation Gains in Group Productivity. H.A.M. Wilke, Status Congruence in Small Groups. J.C. Jesuino, Leadership: Micro-Macro Links. W. Scholl, Effective Teamwork -- A Theoretical Model and a Test in the Field. M. von Cranach, Toward a Theory of the Acting Group. Part III: Interpersonal Influence, Conflict, and Resolution.J.A. Pérez, G. Mugny, The Conflict Elaboration Theory of Social Influence. D. Frey, S. Schulz-Hardt, D. Stahlberg, Information Seeking Among Individuals and Groups and Possible Consequences for Decision Making in Business and Politics. M.A. Hogg, Social Identity, Self-Categorization, and the Small Group. J.M. Rabbie, H.F.M. Lodewijkx, A Behavioral Interaction Model: Toward an Integrative Theoretical Framework for Studying Intra- and Intergroup Dynamics. E.H. Witte, Similarities Among Various Conceptual Positions and Theoretical Points of View.

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Book SynopsisThere is a mysterious connection between our experiences of intimacy--of love, the longing to feel connected, and sexual embrace--and the human sense of time--eternity, impermanence, and rhythm. In this critical analysis of the time-intimacy equation, Bennett shows how the scientific study of personal relationships can address this mystery. As a study of transpersonal science, this book points to the possible evolution of intimacy and of our consciousness of time, and how the two evolutionary paths weave together. Dr. Bennett draws from a wide array of resources to advance and marry two compelling themes: first, the social and clinical science of personal relationships should integrate the spiritual or transpersonal dimension of intimacy, and second, science can contribute to lay understandings by describing the richly temporal aspects of relationships. In blending popular literature, transpersonal psychology, and scientific research and theory, this work also attempts to addrTrade Review"Joel Bennett's Time and Intimacy talks about intimacy in a way that recreates the feeling of intimacy, and recapitulates his vision of an intimate interaction through the structure of the book itself. Just as intimate interactions provide a sense of transcending time even as they can only be understood within a temporary trajectory, Bennett's prose, by refusing linearity and traditional scientific discourse, recapitulates the felt sense of an intimate interaction through its poetic style. Time and Intimacy is a book that can be opened anywhere and enjoyed, as it is composed of many loosely woven strands pulled together graphically and sometimes metaphorically. When it is opened spontaneously and absorbed in bursts, with full attention given to the language itself, it can be appreciated like poetry. Unlike poetry, however, Bennett's work has woven within it references to the latest research on close relationships. For readers who believe that the structure of the text should speak to the subject matter of that text, there is much experimentation with textual structure to be discovered in Time and Intimacy. Language alternates in unpredictable ways between the poetic and the philosophical, between the scientific and the transpersonal, between the objective and the subjective. Much as an intimate conversation itself might, the book invites the reader to transcend the ordinary boundaries of academic disciplines and to think about intimate experience in language that goes beyond ordinary discourse."—Karen PragerUniversity of Texas, Dallas"This book delves deeply and reveals to the reader a rich and new way to look at the realm of relationships. Simultaneously exploring time and intimacy creates a profound shift in our understanding of how people relate. In a modern era that views time as a commodity, intimacy is often lost as relationship suffers. Joel Bennett provides a brilliant approach to a very important subject--well worth any reader's time."—Stephan Rechtschaffen, MDAuthor, Time Shifting: Creating More Time to Enjoy Your Life; Cofounder and CEO,"Bennett has done an extraordinary job of combining three forms of reflection to treat the topic of intimacy. The integration of three themes--quantitative psychology research, transpersonal depth psychology, and temporality/transcendence--constitutes the unique contribution of this book. Time and Intimacy: A New Science of Personal Relationships presents a hypothesis for further reflection in psychology, and it organizes a whole field of research for study. Most important, it deals sensitively with a very important topic."—Robert Cummings NevilleDean, School of Theology, Boston UniversityTable of ContentsContents: S. Duck, Series Editor's Foreword. Preface. Introduction. Intimacy as a Journey Through This Text: Time and Change From Transcription to Transcendence. Unfolding in Time: Intimacy Across Situations. The Forces of Time: The Process of Intimacy. Time, Addiction, and Intimacy: Scripts, Archescripts, & Holoscripts. Temporal Context in Love and Science: The Weave of Temporal Sensitivity. In Search of the Temporal in Personal Relationship Research: From Temporal Initiative to Temporal Scale. Theories of Personal Relationships and the Contextual Model. Summary and Integration: Toward a Transpersonal Science. Appendix.

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Book SynopsisRelational maintenance provides a rallying point for those seeking to discover the behaviors that individuals utilize to sustain their personal relationships. Theoretical models, research programs, and specific studies have examined how people in a variety of close relationships choose to define and maintain those relationships. In addition, relational maintenance turns our attention to communicative processes that help people sustain their close relationships. In this collection, editors Daniel J. Canary and Marianne Dainton focus on the communicative processes critical to the maintenance and enhancement of personal relationships. The volume considers variations in maintaining different types of personal relationships; structural constraints on relationship maintenance; and cultural variations in relational maintenance. Contributions to the volume cover a broad range of relational types, including romantic relationships, family relationships, long-distance relationships, workplace relationships, and Gay and Lesbian relationships, among others. Maintaining Relationships Through Communication: Relational, Contextual, and Cultural Variations synthesizes current research in relationship maintenance, emphasizes the ways that behaviors vary in their maintenance functions across relational contexts, discusses alternative explanations for maintaining relationships, and presents avenues for future research. As such, it is intended for students and scholars studying interpersonal communication and personal relationships.Table of ContentsChapter 1 Definitions and Perspectives on Relational Maintenance Communication, Kathryn Dindia; Part 1 Maintaining Different Types of Relationships; Chapter 2 Maintaining Family Relationships, Sally Vogl-Bauer; Chapter 3 Maintaining Romantic Relationships: A Summary and Analysis of One Research Program, Laura Stafford; Chapter 4 Maintaining Friendships Throughout the Lifespan, Marianne Dainton, Elaine Zelley, Emily Langan; Chapter 5 Maintaining Undesired Relationships, Jon A. Hess; Part 2 Contextual Variations in Maintaining Relationships; Chapter 6 Maintaining Long-Distance Relationships, Brooks A. Aylor; Chapter 7 Computer-Mediated Communication Effects on Relationship Formation and Maintenance, Michael K. Rabby, Joseph B. Walther; Chapter 8 Relationship Maintenance in Organizational Settings, Vincent R. Waldron; Chapter 9 When Part ners Falter: Repair After a Transgression, Tara M. Emmers-Sommer; Part 3 Cultural Variations in Maintaining Relationships; Chapter 10 Relationship Maintenance in Same-Sex Couples, Stephen M. Haas; Chapter 11 Relationship Maintenance in Intercultural Couples: An Interdependence Analysis, Stanley O. Gaines, Jr., Christopher R. Agnew; Chapter 12 Maintaining Marriages in Russia: Managing Societal Influences and Communication Dynamics, Deborah S. Ballard-Reisch, Marat Zaguidoulline, Daniel J. Weigel; Chapter 13 Maintaining Relationships in Korea and the United States: Features of Korean Culture that Affect Relational Maintenance Beliefs and Behaviors, Young-Ok Yum, Daniel J. Canary; Part 4 Epilogue; Chapter 14 Framing the Maintenance of Relationships Through Communication: An Epilogue, Marianne Dainton;

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Book SynopsisThis volume addresses the role of communication in stereotype dynamics, while placing the phenomenon of social stereotypes appropriately in the socio-cultural context.Trade Review"I think it is critically important for social psychologists to focus more on the influence of language and communication across the areas within the discipline, and I believe this volume will stand as a milestone in the movement of social psychology back to studying human interaction." - David Roskos-Ewoldsen, Ph.D., University of Alabama"The authors are all outstanding ... The chapters are timely and important." - Charles Stangor, Ph.D., University of Maryland"… Kashima et al. achieve their goals for this volume… The reader is left with a new appreciation for the social nature of stereotyping, as well as an awareness of the limitations of a strict social cognition perspective… I would recommend this volume for the editors’ intended audience of advanced scholars and students in social psychology, linguistics, and communication." – Matthew L. Newman, PsycCRITIQUES“I think it is critically important for social psychologists to focus more on the influence of language and communication across the areas within the discipline, and I believe this volume will stand as a milestone in the movement of social psychology back to studying human interaction.” —David Roskos-Ewoldsen, Ph.D . University of Alabama“The authors are all outstanding...The chapters are timely and important.” —Charles Stangor, Ph.D. University of MarylandTable of ContentsY. Kashima, K. Fiedler, P. Freytag, Stereotype Dynamics: An Introduction and Overview. Part 1. Stereotype Dynamics.G. Semin, Stereotypes in the Wild. V. Yzerbyt, A. Carnaghi, Stereotype Change in the Social Context. A. Lyons, A. Clark, Y. Kashima, T. Kurz, Cultural Dynamics of Stereotyping. Part 2. Symbolic Mediation and Stereotyping.K. Fiedler, M. Blümke, P. Freytag, S. Koch, C. Unkelbach, A Semiotic Approach to Understanding the Role of Communication in Stereotyping. A. Carnaghi, A. Maass, Derogatory Language in Intergroup Context: Are “Gay” and “Fag” Synonymous? S. Sczesny, J. Bosak, A.B. Diekman, J. Twenge, Dynamics of Sex Role Stereotypes. Part 3. Stereotype and Language Use.C. Wenneker, D. Wigboldus, Interpersonal Consequences and Intrapersonal Underpinnings of the Linguistic Expectancy Bias. K.M. Douglas, R.M. Sutton, C. McGarty, Strategic Language Use in Interpersonal and Intergroup Communication. P. Freytag, Sender-Receiver-Constellations as a Moderator of Linguistic Abstraction Biases. Part 4. Stereotype Sharedness and Distinctiveness.M. Karasawa, S. Suga, Retention and Transmission of Socially Shared Beliefs: The Role of Linguistic Abstraction in Stereotypic Communication. O. Klein, S. Tindale, M. Brauer, The Consensualization of Stereotypes in Small Groups. F. Pratto, P.J. Hegarty, J.D. Korchmaros, How Communication Practices and Category Norms Lead People to Stereotype Particular People and Groups. Part 5. Identity, Self-Regulation, and Stereotyping.M. Hornsey, Intergroup Sensitivity Effect: Responses to Criticisms of Groups. R.M. Sutton, K.M. Douglas, T.J. Elder, M. Tarrant, Social Identity and Social Convention in Responses to Criticisms of Groups. J. Keller, H. Bless, Communicating Stereotype Expectancies: The Interplay of Stereotype Threat and Regulatory Focus.

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Book SynopsisThe Handbook of Relationship Initiation is the first volume to focus specifically on the very beginning stage of relationships â their origin. In this Handbook, leading scholars on relationships review the literature on various processes related to the initiation of relationships: how people meet, communicate for the first time, and begin to define themselves as being in a relationship. Topics include attraction, mate selection, influence of social networks on relationship initiation, initiation over the internet, hook-ups among young adults, and flirting and opening gambits. In addition, the dark side of relationship initiation is considered, including unwanted relationship pursuit and barriers to relationship initiation including social anxiety.This volume provides an overdue synthesis of the literature on this topic. It is especially timely in view of the growing prevalence on relationship initiation online, through matchmaking and other social networking sites, which has increased awareness that science can be used to understand, create, and facilitate compatible matching.This Handbook provides an essential resource for an interdisciplinary range of researchers and students who study relationships, including social psychologists, communication scientists and scholars of marriage and the family.Trade Review"I am somewhat chagrined to find that after 20 years in the field, I found a great deal that I did not know regarding relationship initiation. ... I strongly suspect that this latest work will be an instant classic. ... I highly recommend the handbook for relationship scholars from a variety of disciplines. It is also appropriate for graduate students and upper level undergraduates." - Gregory D. Morrow, Edinboro University of Pennsylvania, in PsycCRITIQUESTable of ContentsPart 1. Introduction. S. Sprecher, A. Wenzel, J. Harvey, Preface. C. A. Bredow, R. M. Cate, T. L. Huston, Have We Met Before? A Conceptual Model of First Romantic Encounters. B. Fehr, Friendship Formation. D. P. Schmitt, An Evolutionary Perspective on Mate Choice and Relationship Initiation. G. Creasey, P. Jarvis, Attachment Theory and Research: A Special Focus on Relationship Initiation. Part 2. The Process of Relationship Initiation. M. R. Cunningham, A. P. Barbee, Prelude to a Kiss: Nonverbal Flirting, Opening Gambits, and Other Communication Dynamics in the Initiation of Romantic Relationships. L. K. Knoblock, L. E. Miller, Uncertainty and Relationship Initiation. W. A. Afifi, A. A. Lucas, Information Seeking in Initial Stages of Relational Development. V. J. Derlega, B. A. Winstead, K. Greene, Self-Disclosure and Starting a Close Relationship. L. K. Guerrero, P. A. Mongeau, On Becoming "More than Friends": The Transition from Friendship to Romantic Relationship. Part 3. Diverse Contexts of Relationship Initiation. X. B. Arriaga, C. R. Agnew, N. M. Capezza, J. J. Lehmiller, The Social and Physical Environment of Relationship Initiation: An Interdependence Analysis. P. W. Eastwick, E. J. Finkel, Speed-Dating: A Powerful and Flexible Paradigm for Studying Relationship Initiation. K. Y. A. McKenna, MySpace or Your Place: Relationship Initiation and Development in the Wired and Wireless World. S. Sprecher, P. Schwartz, J. Harvey, E. Hatfield, Thebusinessoflove.com: Relationship Initiation at Internet Matchmatching Services. Part 4. Attraction and Other Emotions in Relationship Initiation. J. W. Bruce, W. G. Graziano, Attraction and the Initiation of Relationships: A Review of the Empirical Literature. S. Sprecher, D. Felmlee, Insider Perspectives to Attraction. A. Aron, H. E. Fisher, G. Strong, B. Acevedo, S. Riela, I. Tsapelas, Falling in Love. S. S. Hencrick, C. Hendrick, Satisfaction, Love, and Respect in the Initiation of Romantic Relationships. S. Metts, S. L. Mikucki, The Emotional Landscape of Relationship Initiation. Part 5. Challenges and Problematic Relationship Initiation. E. L. Paul, A. Wenzel, J. H. Harvey, Hookups: A Facilitator or a Barrier to Relationship Initiation and Intimacy Development? M. A. Fine, T. A. Coffelt, L. N. Olson, Romantic Relationship Initiation following Relationship Dissolution. W. R. Cupach, B. H. Spitzberg, "Thanks, but No Thanks…." The Occurrence and Management of Unwanted Relationship Pursuit. A. Wenzel, T. B. Kashdan, Emotional Disturbances and the Initial Stages of Relationship Development: Processes and Consequences of Social Anxiety and Depression. Part 6. Cognitions, Beliefs, and Memories About Relationship Initiation. L. Custer, D. Holmberg, K. Blair, T. L. Orbuch, "So How Did You Two Meet?": Narratives of Relationship Initiation. C. R. Knee, A. L. Bush, Relationship Beliefs and Their Role in Relationship Initiation. S. Tran, J. A. Simpson, G. J. O. Fletcher, The Role of Ideal Standards in Relationship Initiation Processes. G. D. Reeder, Perceptions of Goals and Motives in Romantic Relationships. Part 7. Commentary. D. Perlman, Ending the Beginning of Relationships.

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Book SynopsisSystematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research.Trade ReviewFrom the reviews: "The present momgraphy is the first exposition in book form of this theory and of its major applications. Each section of the book is complemented with exerices; each chapter ends with useful comments, and open problems are suggested throughout. The book leads clearly and rapidly an interested reader from basic results to the research level." ---Zentralblatt MATH "The book is an excellent source for getting familiar with the recent developments in geometric and representation theoretic questions in the theory of algebraic groups, mainly in characteristic p." ---Monatshefte für Mathematik “This is a truly fantastic book. It is the first comprehensive text on Frobenius splitting and its applications to geometry and representation theory. If this was a one-paragraph review, I would say buy the book, study it carefully and then apply the contents to a research project’. The readers (and the reviewer) are in the authors’debt.”(MATHEMATICAL REVIEWS)Table of Contents* Preface * Frobenius Splitting: General Theory * Frobenius Splitting * Schubert Varieties * Splitting and Filtration * Cotangent Bundles of Flag Varieties * Group Embeddings * Hilbert Schemes of Points * Bibliography * Index

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Book SynopsisSome Algebraic Geometry.- Linear Algebraic Groups, First Properties.- Commutative Algebraic Groups.- Derivations, Differentials, Lie Algebras.- Topological Properties of Morphisms, Applications.- Parabolic Subgroups, Borel Subgroups, Solvable Groups.- Weyl Group, Roots, Root Datum.- Reductive Groups.- The Isomorphism Theorem.- The Existence Theorem.- More Algebraic Geometry.- F-groups: General Results.- F-tori.- Solvable F-groups.- Freductive Groups.- Reductive F-Groups.- Classification.Trade ReviewFrom the reviews of the second edition: "[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with algebraic groups over arbitrary fields. Some of the material has not been dealt with before in other texts, such as Rosenlicht's results about solvable groups in Chapter 14, the theorem of Borel and Tits on the conjugacy over the ground field of maximal split tori in an arbitrary linear algebraic group in Chapter 15, and the Tits classification of simple groups over a ground field in Chapter 17. The book includes many exercises and a subject index." –Zentralblatt Math (Review of the Second Edition) "In Linear Algebraic Groups Springer aims at a self-contained treatment of the subject in the title and he certainly succeeds … . each chapter comes equipped with an endnote for a bit of history and context, as well as indications of where to go next. And all of it is done in a very clear style, making for a smooth and readable presentation. … a superb choice for any one wishing to learn the subject and go deeply into it quickly and effectively." (Michael Berg, The Mathematical Association of America, March, 2009)Table of ContentsSome Algebraic Geometry.- Linear Algebraic Groups, First Properties.- Commutative Algebraic Groups.- Derivations, Differentials, Lie Algebras.- Topological Properties of Morphisms, Applications.- Parabolic Subgroups, Borel Subgroups, Solvable Groups.- Weyl Group, Roots, Root Datum.- Reductive Groups.- The Isomorphism Theorem.- The Existence Theorem.- More Algebraic Geometry.- F-groups: General Results.- F-tori.- Solvable F-groups.- Freductive Groups.- Reductive F-Groups.- Classification.

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Book SynopsisThe fundamental idea of geometry is that of symmetry. With that principle as the starting point, this book presents a study of Euclidean geometry. It focuses on transformations of the plane. It contains hundreds of exercises. It is suitable for a one-semester undergraduate course on geometry.Table of ContentsFoundations of geometry in the plane Isometries in the plane: Products of reflections Isometries in the plane: Classification and structure Similarities in the plane Conjugacy and geometric equivalence Applications to plane geometry Symmetric figures in the plane Frieze and wallpaper groups Area, volume, and scaling References Index.

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Book SynopsisThe field of random walks on groups is re-emerging with many new ideas and exciting research. This book contains a comprehensive introduction for researchers new to the field. Despite dealing with cutting-edge research, it is accessible even to new graduate students, with worked examples, exercises, and open problems all included.

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Book SynopsisThis text provides the current state of knowledge on, arguably, one of the most attractive and mysterious mathematical objects: the Monster group. Some 20 experts here share their expertise in this exciting field. Ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.Trade Review'Describing the Monster group mathematical structures is the culmination of decades of work. Just as the largest Mathieu group framed the 24-dimensional Leech lattice, so also that lattice is the foundation for constructing the Moonshine Module and the Monster algebra, through which the Monster has become central in a theory with deep connections to modern physics. The first part of the book is a collection of five papers on the Monster and other algebraic structures, presented by international leaders in the area providing an outsider with the necessary content and concepts. It presents an account of the current status of the theory and available computational tools for studying the Monster and its algebras. The machinery for developing Majorana theory and axial algebras underpinning the Monster is based on Algebraic Combinatorics, to which the second part of this collection is devoted.' Cheryl Praeger, Emeritus Professor, University of Western Australia''Monstrous Moonshine', an unexpected correspondence involving the largest sporadic simple group, the classical modular function, and conformal field theory, was one of the greatest discoveries of the twentieth century. The modern approach, pioneered by Alexander Ivanov, involves Majorana algebras; the theory is clearly explained here. Among other jewels in the book is a geometric discussion of the Freudenthal - Tits 'magic square', linking the exceptional Lie algebras with the real, complex, quaternion and octonion number fields.' Peter Cameron, University of St AndrewsTable of ContentsPart I. The Monster: 1. Lectures on vertex algebras Atsushi Matsuo; 2. 3-Transposition groups arising in vertex operator algebras Hiroshi Yamauchi; 3. On holomorphic vertex operator algebras of central charge 24 Ching Hung Lam; 4. Maximal 2-local subgroups of the Monster and Baby Monster Ulrich Meierfrankenfeld and Sergey Shpectorov; 5. The future of Majorana theory II Alexander A. Ivanov; Part II. Algebraic Combinatorics: 6. The geometry of Freudenthal-Tits magic square Hendrik Van Maldegham; 7. On generation of polar Grassmanisns Ilaria Cardinali, Lucca Giuzzi and Antonio Pasini; 8. Ovoidal maximal subspaces of polar spaces Antonio Pasini and Hendrik Van Maldegham; 9. On the behaviour of regular unipotent elements from subsystem subgroups of type A_n with special highest weights Tatsiana S. Busel and Irina D. Suprunenko; 10. Some remarks on the parameter c_2 for a distance-regular graph with classical parameters Jack H. Koolen, Jongyook Park and Qianqian Yang; 11. Distance-regular graphs, the subconstituent algebra, and the q-polynomial property Paul Terwilliger; 12. Terwilliger algebras and the Weisfeiler-Leman stabilization Tatsuro Ito; 13. Extended doubling of self-complementary strongly regular graphs and an analogue for digraphs Takuya Ikuta and Akihiro Munemasa; 14. Using GAP package for research in graph theory, design theory and finite geometries Leonard H. Soicher.

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Book SynopsisThis book differentiates between categories of adolescent male offending and explores the behavioural and social profiles of those who become involved inviolent offending and organized crime. Using self-reported and arrest data, the book examines the key stages of male adolescent offending with a view to early recognition of behaviours that leave young men vulnerable to criminal exploitation and the escalation of violence. It also explains the importance of understanding crime motivations, how young men view themselves when they offend, and the emotions that they experience. Rather than looking at violent offending as a single category of behavior, the book helps readers differentiate between types of adolescent violence and understand the underlying psychological and social causes. It offers an insight into the journey of young people who are criminally exploited and those who become involved in committing acts of serious violence and organized crime. It does so by using data from Table of ContentsIntroductionChapter 1 Adolescent offending profilesChapter 2 Substance use and drug offensesChapter 3 Expressive violenceChapter 4 Knife crimeChapter 5 Sensation seekingChapter 6 Acquisitive offendingChapter 7 Criminal groups and exploitationConclusion

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Book SynopsisThe Psychology of Collective Narcissism is a ground-breaking text that presents a new theory of collective narcissism, a belief that exaggerated greatness of one's own group should be but is not sufficiently appreciated by others.The book presents this concept against the background of social identity theory and research. It explores antecedent as well as social and political consequences of collective narcissism. The author discusses how this burgeoning theory and research can help to elucidate a wide range of psychological dynamics involved in pressing societal issues, such as the declining appeal of democracy, increasing populism, decreasing social solidarity, increasing societal polarization and prejudice, intergroup hostility and political violence, social inequality, and fake news and belief in conspiracy theories. Also referring to societal problems exacerbated by the COVID-19 pandemic, this highly topical work explores socially shared beliefs as risk factors Table of ContentsAcknowledgementsIntroduction: Psychology of collective narcissism How does narcissism become collective? ‘Dark side of ingroup love’: Collective narcissism and ingroup identification National narcissism, nationalism, and patriotism Collective narcissism, intergroup threat, and intergroup hate Collective narcissism and prejudice: Politics of hate Collective narcissism and social exclusion Collective narcissism of populism ‘Revolutionaries in reverse’: Collective narcissism and political orientation Collective narcissism and pursuit of equality ‘To the point of irrationality’: Collective narcissism and conspiracy theories

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Book SynopsisPeople Skills for Behavior Analysts provides a much-needed introduction to the people skills needed to succeed as a behavior analyst.Divided into two primary parts Foundational Skills and Specialized Skills this book addresses an impressive breadth of people skills, focusing on intrapersonal and interpersonal skills, collaboration, consultation and training, leadership, and resource development. Relying on recent evidence-based practices and relevant literature tailored to meet the new BACB Task List, Professional & Ethical Compliance Code, and Supervised Independent Fieldwork requirements, the text includes contributions from leading figures from a wide variety of applied behavior analysis subfields to provide a truly balanced overview. The book delves into the literature from fields related to behavior analysis, such as counselling, psychology, graphic design, management and education, and applies these perspectives to behavioral theories and principles to provide Table of ContentsPart I: Foundational Skills Chapter 1: Intrapersonal Skills 1.1 The Importance of Intrapersonal Skills for Behavior Analysts 1.2 The Discerning ABA Practitioner 1.3 Self-Care for Behavior Analysts: A guide to eating fewer doughnuts and taking more naps Chapter 2: Interpersonal Skills 2.1 20 Key Behaviors for Rapport Building 2.2 Cultural Competence in Communication 2.3 A Critical Look at Autism 2.4 Accepting Feedback Makes the World Go ‘Round: From Student to Practitioner 2.5 How to Teach Rapport Building Skills to Behavior Analysts Chapter 3: Collaboration 3.1 No More “Train And Train More”: A Functional, Contextual Approach to Collaboration with Families 3.2 Playing Nicely in the Interdisciplinary Sandbox: A How to Guide on Effective Collaboration with Various Professionals 3.3 Whose the King of the Castle? Collaborating with Educators and Schools as a Behavior Analyst 3.4 Overcoming the Aversive: Handling Difficult Conversations with Professionalism and Compassion 3.5 Running Efficient and Effective Meetings with Collaboration and Compassion Part 2: Specialized Skills Chapter 4: Consultation & Training 4.1 Don’t Blame the Mediator: Keeping Applied Behavior Analysis Doable for Best Possible Outcomes 4.2 Beyond the PowerPoint: Becoming an Engaging Presenter 4.3 Behavior Analyst as Changemaker: Science, Advocacy and Activism in Practice 4.4 Using Movement Education, Motor Learning, and Phenomenology to Inform Teaching Strategies in Other Professional Contexts Chapter 5: Leadership 5.1 It’s Not You, It’s Us: Fostering a Behavior Analytical Supervisor/Supervisee Relationship 5.2 People Skills for Behavior Analysis: Putting the Super in Your Supervisory Relationships 5.3 Giving Performance Feedback that Makes a Difference 5.4 Interviewing Strategies: Integrating Practices from Industrial/Organizational Psychology into Behavior Analysis for Successful Hiring Chapter 6: Innovative, Creative Ways to use ABA 6.1 Making Applied Behavior Analysis Accessible to Consumers 6.2 Telehealth to Implement Applied Behavior Analysis 6.3 You’re on mute! People skills behind the screens and behind the scenes 6.4 Making a Document People will Actually Read 6.5 A Trauma-Informed Approach to Behavior Analysis 6.6 Behavior analysts' skills for co-developing virtual reality game-based technologies as applied behavior analysis programs for autistic adults

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This book attempts to shake up' the current complacency around therapy and mental health' behaviours by putting therapy fully into context using Social Contextual Analysis; showing how changes to our social, discursive, and societal environments, rather than changes to an individual's mind', will reduce suffering from the mental health' behaviours.Guerin challenges many assumptions about both current therapy and psychology, and offers alternative approaches, synthesized from sociology, social anthropology, sociolinguistics, and elsewhere. The book provides a way of addressing the mental health' behaviours including actions, talking, thinking, and emotions, by taking people's external life situations into account, and not relying on an imagined internal source'. Guerin describes the broad contexts for current Western therapies, referring to social, discursive, cultural, societal, and economic contexts, and suggests that we need to research the components of therapies an

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Book SynopsisThis fascinating book explores the concept of slow living, offering a philosophical and psychological exploration of the need for a slower pace of life. It advocates for reclaiming and rediscovering more natural and human ways of being.In a digital age, which is dominated by an increasingly tyrannical trinity of speed, efficiency and productivity, the author challenges the pernicious ideal of instant gratification, perpetuated by modern consumer culture. This book examines alternative ways of being through re-examining the Wisdom Traditions of Hinduism, Buddhism, Daoism and Judaism through an ongoing and engaging dialogue with psychology and psychotherapy, including insights from environmental psychology, ecopsychology and cyberpsychology. The book argues against the trend for personal responsibility, adaptability and resilience, and the idea that stress is the new normal.' Instead, it proposes a radical shift in paradigm, promoting not for collectively rising up and ove

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The Handbook of Communication Skills is recognised as one of the core texts in the field of communication, offering a state-of-the-art overview of this rapidly evolving field of study.The fifth edition of this bestselling book situates communication in a range of different contexts, from interacting in groups to the counselling interview. It covers topics such as non-verbal behaviour, listening, negotiation, interacting in groups, and mentoring. This new edition has been fully revised and updated, and includes a brand new chapter on digitally mediated communications in social and working environments, as well as newly written chapters on humour and laughter in communication, and persuasion. Based on the core tenet that interpersonal communication can be conceptualised as a form of skilled activity, the book looks at core communication skills and how these can be applied in specific contexts, expertly combining theory with practice.This handbook provides a rich m

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Book SynopsisReligious Hatred and Human Conflict focuses the lens of psychodynamic psychology on a phenomenon that often confounds conventional thinking the intensity of conflict with religious or quasi-religious dimensions.The book highlights six dimensions of religion: identity, doctrine and practice, emotion and experience, mythology, sacred values and power and control, exploring how these can give rise to religious hatred and lead to marginalisation, persecution and even genocide. It also explores reasons for the evolution of religion and religious hatred, and their relationship with human behaviour through contemporary issues such as fundamentalism, martyrdom, clerical narcissism and apocalyptic belief. Acland examines how religious hatred and conflict may be transcended by facilitating processes of dialogue and diapraxis which enable a systematic understanding of prejudices and projections. Last, it offers practical methods and strategies for helping individTrade Review'It is a unique publication and it fills an important practical and theoretical gap in the existing literature … It is innovative and refreshing that the author integrates psychodynamic perspectives into the work – this is an important lacuna in the literature. The work fills a gap by approaching the question of religious hatred and conflict with religious dimensions from multiple different conceptual angles, many of which are much neglected in the field.' - David Leech, Senior Lecturer, Dept of Religion and Theology, University of Bristol, UKTable of ContentsPART 1: Contexts and culturesChapter 1: Beginning, background and biasesChapter 2: Three backstoriesConflict resolution and transformationThe psychology of religionPsychodynamic psychologyInspirational beginnings: Sigmund Freud and Carl JungRehabilitating JungBeyond Freud and JungPART 2: What is religious hatred? Chapter 3: Thinking about religious hatredAnatomies of hatredHatred and evolutionHatred and the OtherFrom hatred to genocideHatred and thoughtcrimeReligion and hatred as addictionsChapter 4: Psychodynamic approaches to religious hatredComplexesComplexes and religious traditionsCultural complexesThe ShadowComplexes and Shadows in transmissionPART 3: Religious hatred and the dimensions of religion Chapter 5: Six dimensions of religionDimensions of religionThe dimensions of religion, religious hatred and the problem of evilChapter 6: The identity dimensionReligion and identityConflicting religious identities and the idea of the "Other"The narcissism of small differencesThe Persona, the Shadow and the OtherChapter 7: The doctrine and practice dimensionReligious doctrine and the Golem EffectFundamentalismFundamentalism, hatred and violenceThe psychology of fundamentalist doctrine and practiceGroups and group practicesFundamentalism as a form of cultural complexChapter 8: The emotional and experiential dimensionThe missing dimensionMarks of religious experienceEmotions and religious experienceThe psychology of religious experienceReligious hatred and the Divided SelfHealing the Divided SelfReligious hatred as the failure to individuateHatred and the Self Chapter 9: The mythological dimensionApproaching mythologySocial impacts of mythImpacts of myth on individualsMythology and religious hatredModern mythsCosmic warsWhen myth leads to martyrdomThe psychology of ArmageddonMythmaking and scapegoatingChapter 10: The sacred values dimensionThe nature of sacred valuesSacred values and personal motivationValuing sacred valuesPseudo-sacred valuesSecular values that turn sacredSacred values and religious hatredSacred values and uncertaintyChapter 11: The power and control dimensionThe impetus to controlConstraints as controlCompensatory controlTerror Management TheoryFrom control to paranoiaControl through clericalismEvolution of religious controlPART 4: Working through religious hatredChapter 12: The search for answersUnderstanding religionAppreciating the emotional and unconsciousBeyond dialogueRe-framing religious hatred as a psychospiritual problemIncorporating the transcendent functionThe practicalities of conflict resolution: dialogue and diapraxisDiapraxis: process and structuresUsing the dimensions of religion as a structure for dialogue and diapraxis AfterwordReferencesIndex

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Book SynopsisHow do we find the courage to act together against the climate crisis? This book weaves together real-life findings and examples from the socio-ecological movement with psychological research to show how motivation for collective climate action can be built.The book addresses two key questions: how can individuals be motivated to participate in collective climate action, and how can climate groups become resilient and effective? Specifically, it explores how individuals can foster their identification with climate action groups and the belief in their joint efficacy. It touches on a wide range of topics, covering anger, moral considerations, activist burnout, and the perception of protests, as well as general theories of socio-ecological change.This book is for anyone who is seeking the courage to act together and is curious about psychological insights. It will be essential reading for climate and environmental practitioners, climate activists and campaigners, climate change communicators, and anyone involved in socio-ecological change. It will also be of interest to students and researchers in the fields of environmental psychology, climate change, collective action, and political psychology.The Open Access version of this book, available at http://www.taylorfrancis.com, has been made available under a Creative Commons (CC BY) 4.0 license.

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