Algebraic geometry Books

Book Synopsis"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution.Trade ReviewFrom the reviews:“Sotirios E. Louridas and Michael Th. Rassias, the authors of the book at hand, put together an excellent collection of problems for practice. They provide detailed solutions following the masters of that skill. … an active reader would greatly benefit from reading the book; while working out the problems is bound to sharpen his or her problem solving skills. … it’s a worthy addition to a library of a problem solver.” —Alex Bogomolny, MAA Reviews, December, 2013"The book is a wonderful presentation of the essential concepts, ideas and results of Euclidean Geometry useful in solving olympiad problems of various level of difficulties. The theoretical part is excellently illustrated by challenging olympiad problems. The complete solutions to these problems are carefully presented, most of them together with several interesting comments and remarks. ... All in all the text is a highly recommendable choice for any olympiad training program, and fills some gaps in the existing literature in Euclidean Geometry. The book is a very useful source of models and ideas for students, teachers, heads of national teams and authors of problems, as well as for people who are interested in mathematics and solving difficult problems."—Mihaly Bencze, EMS Newsletter, November 2013"A subject of high interest for problem-solving in Euclidean Geometry is the application of geometric transformations ... The authors have succeeded to study with great accuracy these transformations. Additionally, they have applied them in order to obtain very nice solutions for some quite challenging problems ... The book is full of new and challenging ideas that will provide guidance and inspiration for future study in the fundamental area of Euclidean Geometry. The large collection of problems in this book provides a valuable recourse for advanced high school students, university undergraduates, instructors, and Mathematics coaches preparing students to participate in mathematical Olympiads...."—Nicusor Minculete, Gazeta Matematică, Seria B., 10/2013"This book provides an essential presentation of concepts and ideas as well as problems with their solutions in Euclidean Geometry, a traditional and still challenging part of Geometry.—Dorian Andrica, Zentralblatt"The book is mainly devoted to several very interesting problems, some of which constructed by the authors, that have been presented in a rigorous and self-contained manner. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. The book will be of particular interest to students and teachers who train them for Mathematical Olympiads and other Mathematical Contests. Additionally to everyone who enjoys studying some of the jewels of Euclidean Geometry and has some special love for good problems and beautiful ideas. ... The Foreword of the book has been written by Michael H. Freedman (Fields Medal in Mathematics, 1986) ... The authors deserve congratulations for their excellent effort and success to provide a high quality service in fundamental mathematics. " —Jose Luis Diaz Barrero, Octogon Mathematical Magazine, October 2013"Sixty-five problems and their solutions are arranged in three parts: problems based on basic theory, problems based on advancedtheory, and geometric inequalities. Some problems were included in International Mathematical Olympiads (IMOs) or proposed in short lists in IMOs ... the problem part of the book ... contains a collection of interesting problems. ... Chapter 4 seeks to "present some of the most essential theorems of Euclidean Geometry". Some of these theorems (Pythagoras', Ceva's, Menelaus') are important indeed and applicable to many problems."—Yury J. Ionin, Mathematical Reviews, January 2014"There are many excellent books on plane Euclidean geometry, exploring the subject at various levels. The book under review, which is foreworded by Michael H. Freedman (Fields Medal, 1986), adds yet another facet to this colorful subject. This delightful book presents a collection of problems in plane Euclidean geometry in the spirit of mathematical olympiads, along with their solutions. Additionally, it provides essential theory of plane Euclidean geometry, with proofs of some fundamental theorems. As such, this monograph is an excellent training manual to use in preparation for mathematical competitions and olympiads. Hence, this is a book that belongs in all academic libraries, from high school through graduate level." —Abraham A. Ungar, Acta Universitatis Apulensis, 40/2014.Table of ContentsForeword.- Preface.- Basic Concepts and Theorems of Euclidean Geometry.- Methods of Analysis, Synthesis, Construction and Proof.-Geometrical Constructions.- Geometrical Loci.- Problems of Olympiad Caliber.- Solutions of the Problems.- Bibliography.- Index.

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Book SynopsisThis book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.Table of Contents1. On fine gradings on central simple algebras 2. On observable module categories 3. Group gradings on integral group rings 4. Profinite graphs – comparing notions 5. Lie identities in symmetric elements in group rings: A survey 6. Irreducible morphisms in subcategories 7. Bol loops with a unique nonidentity commutator/associator 8. Weil representations of symplectic groups 9. Gradings and graded identities for the upper triangular matrices over an infinite field 10. Structure of some classes of repeated-root constacyclic codes over integers modulo 2m 11. Units in noncommutative orders 12. Idempotents in group algebras and coding theory 13. Finitely generated constants of free algebras 14. Partial actions of groups on semiprime rings 15. Representations of affine Lie superalgebras 16. On algebras and superalgebras with linear codimension growth 17. On spectra of group rings of finite abelian groups 18. Wedderburn decomposition of small rational group algebras 19. Some questions on skewfields 20. On the role of rings and modules in algebraic coding theory 21. Semiperfect rings with T-nilpotent prime radical 22. The structure of the baric algebras 23. On torsion units of integral group rings of groups of small order 24. On a conjecture of Zassenhaus for metacyclic groups 25. Nilpotent blocks revisited 26. Decomposition of central units of integral group rings 27. Generic units in ZC 28. On quasi-Frobenius semigroup algebras 29. Twisted loop algebras and Galois cohomology 30. Presentation of the group of units of ZD 31. Engel theorem for Jordan rational group algebras.

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Book SynopsisEasily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)Trade ReviewFrom the reviews: "The book under review provides an introduction to the contemporary theory of compact complex manifolds, with a particular emphasis on Kähler manifolds in their various aspects and applications. As the author points out in the preface, the text is based on a two-semester course taught in 2001/2002 at the University of Cologne, Germany. Having been designed for third-year students, the aim of the course was to acquaint beginners in the field with some basic concepts, fundamental techniques, and important results in the theory of compact complex manifolds, without being neither too basic nor too sketchy. Also, as complex geometry has undergone tremendous developments during the past five decades, and become an indispensable framework in modern mathematical physics, the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field, too, up to some of the fascinating aspects of the stunning interplay between complex geometry and quantum field theory in theoretical physics. The present text, as an outgrowth of this special course in complex geometry, does evidently reflect these emphatic intentions of the author's in a masterly manner. Keeping the prerequisites from complex analysis and differential geometry to an absolute minimum, he provides a streamlined introduction to the theory of compact complex manifolds and Kählerian geometry, with many outlooks and applications, but without trying to be encyclopedic or panoramic. without trying to be encyclopedic or panoramic. As to the precise contents, the text consists of six chapters and two appendices. [...] The author has added two general appendices at the end of the book. Those aremeant to help the unexperienced reader to recall a few basic concepts and facts from differential geometry, Hodge theory on differentiable manifolds, sheaf theory, and sheaf cohomology. This very user-friendly service makes the entire introductory text more comfortable for less seasoned students, perhaps also for interested and mathematically less experienced physicists, although the author does not claim absolute self-containedness of the book. The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints for further reading, outlooks to other directions of research, and numerous exercises after each section. The exercises are far from being bland and often quite demanding, but they should be mastered by ambitious and attentive readers, in the last resort after additional reading. Finally, there is a very rich bibliography of 118 references, also from the very recent research literature, which the author profusely refers to throughout the entire text. The whole exposition captivates by its clarity, profundity, versality, and didactical strategy, which lead the reader right to the more advanced literature in complex geometry as well as to the forefront of research in geometry and its applications to mathematical physics. No doubt, this book is an outstanding introduction to modern complex geometry." KIeinert (Berlin), Zentralblatt für Mathematik 1055 (2005) This is a very interesting and nice book. It provides a clear and deep introduction about complex geometry, namely the study of complex manifolds. These are differentiable manifolds endowed with the additional datum of a complex structure that is more rigid than the geometrical structures used in differential geometry. Complex geometry is on the crossroad of algebraic and differential geometry. Complex geometry is also becoming a stimulating and useful tool for theoretical physicists working in string theory and conformal field theory. The physicist, will be very glad to discover the interplay between complex geometry and supersymmetry and mirror symmetry. The book begins by explaining the local theory and all you need to understand the global structure of complex manifolds. Then we get an introduction to the complex manifolds as such, where the reader can progressively perceive the difference between real manifolds and complex ones. Then he gets an account of the theory of Kälher manifolds. And the physicist will be glad to find therein a first step on the road going from complex geometry to conformal field theory and supersymmetry. One chapter is dedicated to the study of holomorphic vector bundles (connections, curvature, Chern classes). In this context, the reader will clarify the relations between Riemannian and Kälher geometries. With all this stuff it is then possible to focus on some applications of cohomology. This leads to a nice introduction to the famous Hirzebruch-Riemann-Roch theorem and to Kodaira vanishing and embedding theorems. The last chapter of the book tackles the very important topics of deformations of complex structures. This chapter will be interesting especially for readers that are studying Calabi-Yau manifolds and mirror symmetries. The main text of the book is completed by two pedagogical appendices. One about Hodge theory and the other about sheaf cohomology. Thus this beautiful textbook will be very interesting for both pure mathematicians and theoretical physicists working in recent domains of field theory. It can be used by students or scientists for a first introduction in this field. It is always very accessible and the reader will find a detailed account of the basic concepts and many well-chosen exercises that illustrate the theory. Many illuminating examples help the reader in the understanding of all fundamental notions. I could certainly recommend this textbook to my students attending my lectures on differential geometry. Professor Dominique LAMBERT, University of Namur; Department « sciences, philosophies et sociétés » Rue de Bruxelles 61 B-5000 Namur Belgium "As complex geometry has undergone tremendous developments … the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field … . This very user-friendly … more comfortable for less seasoned students … . The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints … . Finally, there is a very rich bibliography … . The whole exposition captivates by its clarity, profundity, versality, and didactical strategy … . an outstanding introduction to modern complex geometry." (Werner Kleinert, Zentralblatt Math, Vol. 1055, 2005) "The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions." (L’Enseignment Mathematique, Vol. 50 (3-4), 2004) "This is the book that a generation of complex geometers will wish had existed when they first learned the subject, and that the next generation of geometers will surely use. … Inserted into the standard material are some excellent appendices to stimulate interest and further reading … . the reader learning the basic material is brought quickly and often to some fascinating areas of current research. Exercises introduce many examples … . The result is an excellent course in complex geometry." (Richard P. Thomas, Mathematical Reviews, 2005h) "The book is based on a year course on complex geometry and its interaction with Riemannian geometry. It prepares a basic ground for a study of complex geometry as well as for understanding ideas coming recently from string theory. … The book is a very good introduction to the subject and can be very useful both for mathematicians and mathematical physicists." (EMS Newsletter, June, 2005) "The book under review is a textbook, based on a 2-semester course to third year undergraduates in the University of Cologne. … In the UK I think the book would be regarded as more suitable for a masters’ level course for students well versed in standard complex analysis and differential geometry." (Peter Giblin, The Mathematical Gazette, Vol. 91 (520), 2007)Table of ContentsLocal Theory.- Complex Manifolds.- Kähler Manifolds.- Vector Bundles.- Applications of Cohomology.- Deformations of Complex Structures.

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Book SynopsisProvides an easy to understand mathematical tool set for professionals an students in electromagnetic study Non-axiomatic, non-challenging, less formal tutorial approach on the subject Includes appendices with reference material that includes a helpful glossary of terms .Trade Review"This book will benefit scientists and engineers who use electromagnetic theory in the course of their work.” (Zentralblatt MATH, 1 May 2013)Table of ContentsPreface xi Reading Guide xv 1. Introduction 1 2. A Quick Tour of Geometric Algebra 7 2.1 The Basic Rules of a Geometric Algebra 16 2.2 3D Geometric Algebra 17 2.3 Developing the Rules 19 2.3.1 General Rules 20 2.3.2 3D 21 2.3.3 The Geometric Interpretation of Inner and Outer Products 22 2.4 Comparison with Traditional 3D Tools 24 2.5 New Possibilities 24 2.6 Exercises 26 3. Applying the Abstraction 27 3.1 Space and Time 27 3.2 Electromagnetics 28 3.2.1 The Electromagnetic Field 28 3.2.2 Electric and Magnetic Dipoles 30 3.3 The Vector Derivative 32 3.4 The Integral Equations 34 3.5 The Role of the Dual 36 3.6 Exercises 37 4. Generalization 39 4.1 Homogeneous and Inhomogeneous Multivectors 40 4.2 Blades 40 4.3 Reversal 42 4.4 Maximum Grade 43 4.5 Inner and Outer Products Involving a Multivector 44 4.6 Inner and Outer Products between Higher Grades 48 4.7 Summary So Far 50 4.8 Exercises 51 5. (3+1)D Electromagnetics 55 5.1 The Lorentz Force 55 5.2 Maxwell’s Equations in Free Space 56 5.3 Simplifi ed Equations 59 5.4 The Connection between the Electric and Magnetic Fields 60 5.5 Plane Electromagnetic Waves 64 5.6 Charge Conservation 68 5.7 Multivector Potential 69 5.7.1 The Potential of a Moving Charge 70 5.8 Energy and Momentum 76 5.9 Maxwell’s Equations in Polarizable Media 78 5.9.1 Boundary Conditions at an Interface 84 5.10 Exercises 88 6. Review of (3+1)D 91 7. Introducing Spacetime 97 7.1 Background and Key Concepts 98 7.2 Time as a Vector 102 7.3 The Spacetime Basis Elements 104 7.3.1 Spatial and Temporal Vectors 106 7.4 Basic Operations 109 7.5 Velocity 111 7.6 Different Basis Vectors and Frames 112 7.7 Events and Histories 115 7.7.1 Events 115 7.7.2 Histories 115 7.7.3 Straight-Line Histories and Their Time Vectors 116 7.7.4 Arbitrary Histories 119 7.8 The Spacetime Form of ∇ 121 7.9 Working with Vector Differentiation 123 7.10 Working without Basis Vectors 124 7.11 Classifi cation of Spacetime Vectors and Bivectors 126 7.12 Exercises 127 8. Relating Spacetime to (3+1)D 129 8.1 The Correspondence between the Elements 129 8.1.1 The Even Elements of Spacetime 130 8.1.2 The Odd Elements of Spacetime 131 8.1.3 From (3+1)D to Spacetime 132 8.2 Translations in General 133 8.2.1 Vectors 133 8.2.2 Bivectors 135 8.2.3 Trivectors 136 8.3 Introduction to Spacetime Splits 137 8.4 Some Important Spacetime Splits 140 8.4.1 Time 140 8.4.2 Velocity 141 8.4.3 Vector Derivatives 142 8.4.4 Vector Derivatives of General Multivectors 144 8.5 What Next? 144 8.6 Exercises 145 9. Change of Basis Vectors 147 9.1 Linear Transformations 147 9.2 Relationship to Geometric Algebras 149 9.3 Implementing Spatial Rotations and the Lorentz Transformation 150 9.4 Lorentz Transformation of the Basis Vectors 153 9.5 Lorentz Transformation of the Basis Bivectors 155 9.6 Transformation of the Unit Scalar and Pseudoscalar 156 9.7 Reverse Lorentz Transformation 156 9.8 The Lorentz Transformation with Vectors in Component Form 158 9.8.1 Transformation of a Vector versus a Transformation of Basis 158 9.8.2 Transformation of Basis for Any Given Vector 162 9.9 Dilations 165 9.10 Exercises 166 10. Further Spacetime Concepts 169 10.1 Review of Frames and Time Vectors 169 10.2 Frames in General 171 10.3 Maps and Grids 173 10.4 Proper Time 175 10.5 Proper Velocity 176 10.6 Relative Vectors and Paravectors 178 10.6.1 Geometric Interpretation of the Spacetime Split 179 10.6.2 Relative Basis Vectors 183 10.6.3 Evaluating Relative Vectors 185 10.6.4 Relative Vectors Involving Parameters 188 10.6.5 Transforming Relative Vectors and Paravectors to a Different Frame 190 10.7 Frame-Dependent versus Frame-Independent Scalars 192 10.8 Change of Basis for Any Object in Component Form 194 10.9 Velocity as Seen in Different Frames 196 10.10 Frame-Free Form of the Lorentz Transformation 200 10.11 Exercises 202 11. Application of the Spacetime Geometric Algebra to Basic Electromagnetics 203 11.1 The Vector Potential and Some Spacetime Splits 204 11.2 Maxwell’s Equations in Spacetime Form 208 11.2.1 Maxwell’s Free Space or Microscopic Equation 208 11.2.2 Maxwell’s Equations in Polarizable Media 210 11.3 Charge Conservation and the Wave Equation 212 11.4 Plane Electromagnetic Waves 213 11.5 Transformation of the Electromagnetic Field 217 11.5.1 A General Spacetime Split for F 217 11.5.2 Maxwell’s Equation in a Different Frame 219 11.5.3 Transformation of F by Replacement of Basis Elements 221 11.5.4 The Electromagnetic Field of a Plane Wave Under a Change of Frame 223 11.6 Lorentz Force 224 11.7 The Spacetime Approach to Electrodynamics 227 11.8 The Electromagnetic Field of a Moving Point Charge 232 11.8.1 General Spacetime Form of a Charge’s Electromagnetic Potential 232 11.8.2 Electromagnetic Potential of a Point Charge in Uniform Motion 234 11.8.3 Electromagnetic Field of a Point Charge in Uniform Motion 237 11.9 Exercises 240 12. The Electromagnetic Field of a Point Charge Undergoing Acceleration 243 12.1 Working with Null Vectors 243 12.2 Finding F for a Moving Point Charge 248 12.3 Frad in the Charge’s Rest Frame 252 12.4 Frad in the Observer’s Rest Frame 254 12.5 Exercises 258 13. Conclusion 259 14. Appendices 265 14.1 Glossary 265 14.2 Axial versus True Vectors 273 14.3 Complex Numbers and the 2D Geometric Algebra 274 14.4 The Structure of Vector Spaces and Geometric Algebras 275 14.4.1 A Vector Space 275 14.4.2 A Geometric Algebra 275 14.5 Quaternions Compared 281 14.6 Evaluation of an Integral in Equation (5.14) 283 14.7 Formal Derivation of the Spacetime Vector Derivative 284 References 287 Further Reading 291 Index 293 The IEEE Press Series on Electromagnetic Wave Theory

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Book SynopsisThe author introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise.Trade Review"It is clear that this book presents highly important new views and results on the classical theory of complex linear differential equations."--Zentralblatt fur MathematikTable of Contents* First results on rigid local systems * The theory of middle concolution * Fourier Transform and rigidity * Middle concolution: dependence on parameters * Structure of rigid local systems * Existence algorithms for rigids * Diophantine aspects of rigidity * rigids

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Book SynopsisDescribes some major advances made in algebraic topology, centering on the nilpotence and periodicity theorems. This book begins with some elementary concepts of homotopy theory that are needed to state the problem. The latter portion provides specialists with a coherent and rigorous account of the proofs.Trade Review"Familiarity with the material of this book is essential for any a serious homotopy theorist... [The author's] important role in the developments will ensure that [this book] will remain an important source for some time."--Bulletin of the London Mathematical SocietyTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*Introduction, pg. xiii*Chapter 1. The main theorems, pg. 1*Chapter 2. Homotopy groups and the chromatic filtration, pg. 11*Chapter 3. MU-theory and formal group laws, pg. 25*Chapter 4. Morava's orbit picture and Morava stabilizer groups, pg. 37*Chapter 5. The thick subcategory theorem, pg. 45*Chapter 6. The periodicity theorem, pg. 53*Chapter 7. Bousfield localization and equivalence, pg. 69*Chapter 8. The proofs of the localization, smash product and chromatic convergence theorems, pg. 81*Chapter 9. The proof of the nilpotence theorem, pg. 99*Appendix A. Some tools from homotopy theory, pg. 119*Appendix B. Complex bordism and BP-theory, pg. 145*Appendix C. Some idempotents associated with the symmetric group, pg. 183*Bibliography, pg. 195*Index, pg. 205

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Book SynopsisTrade Review"John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters""John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society"Table of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii* 1. Smooth Manifolds, pg. 1* 2. Vector Bundles, pg. 13* 3. Constructing New Vector Bundles Out of Old, pg. 25* 4. Stiefel-Whitney Classes, pg. 37* 5. Grassmann Manifolds and Universal Bundles, pg. 55* 6. A Cell Structure for Grassmann Manifolds, pg. 73* 7. The Cohomology Ring H*(Gn; Z/2), pg. 83* 8. Existence of Stiefel-Whitney Classes, pg. 89* 9. Oriented Bundles and the Euler Class, pg. 95* 10. The Thom Isomorphism Theorem, pg. 105* 11. Computations in a Smooth Manifold, pg. 115* 12. Obstructions, pg. 139* 13. Complex Vector Bundles and Complex Manifolds, pg. 149* 14. Chern Classes, pg. 155* 15. Pontrjagin Classes, pg. 173* 16. Chern Numbers and Pontrjagin Numbers, pg. 183* 17. The Oriented Cobordism Ring OMEGA*, pg. 199* 18. Thom Spaces and Transversality, pg. 205* 19. Multiplicative Sequences and the Signature Theorem, pg. 219* 20. Combinatorial Pontrjagin Classes, pg. 231*Epilogue, pg. 249*Appendix A: Singular Homology and Cohomology, pg. 257*Appendix B: Bernoulli Numbers, pg. 281*Appendix C: Connections, Curvature, and Characteristic Classes, pg. 289*Bibliography, pg. 315*Index, pg. 325

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Book SynopsisResolution of singularities is a powerful and frequently used tool in algebraic geometry. This book provides a comprehensive treatment of the characteristic 0 case. It describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether.Trade Review"Throughout his lectures, Kollar uses plenty of motivations and examples, and the text is very readable. Any graduate student or mathematicians who wishes to learn about the subject would be well-served to use this book as a starting point."--Darren Glass, MAA Review "People are already using this book. I am using this book now. I expect it will be used well into the future."--Dan Abramovich, Mathematical Reviews "The book will be an invaluable tool not only for graduate student, but also for algebraic geometers. Mathematicians working in different fields will also enjoy the clarity of the exposition and the wealth of ideas included. This will become, I'm sure, as it happened to most books in this series, one of the classics of modern mathematics."--Paul Blaga, MathematicaTable of ContentsIntroduction 1 Chapter 1. Resolution for Curves 5 1.1. Newton's method of rotating rulers 5 1.2. The Riemann surface of an algebraic function 9 1.3. The Albanese method using projections 12 1.4. Normalization using commutative algebra 20 1.5. Infinitely near singularities 26 1.6. Embedded resolution, I: Global methods 32 1.7. Birational transforms of plane curves 35 1.8. Embedded resolution, II: Local methods 44 1.9. Principalization of ideal sheaves 48 1.10. Embedded resolution, III: Maximal contact 51 1.11. Hensel's lemma and the Weierstrass preparation theorem 52 1.12. Extensions of K((t)) and algebroid curves 58 1.13. Blowing up 1-dimensional rings 61 Chapter 2. Resolution for Surfaces 67 2.1. Examples of resolutions 68 2.2. The minimal resolution 73 2.3. The Jungian method 80 2.4. Cyclic quotient singularities 83 2.5. The Albanese method using projections 89 2.6. Resolving double points, char 6= 2 97 2.7. Embedded resolution using Weierstrass' theorem 101 2.8. Review of multiplicities 110 Chapter 3. Strong Resolution in Characteristic Zero 117 3.1. What is a good resolution algorithm? 119 3.2. Examples of resolutions 126 3.3. Statement of the main theorems 134 3.4. Plan of the proof 151 3.5. Birational transforms and marked ideals 159 3.6. The inductive setup of the proof 162 3.7. Birational transform of derivatives 167 3.8. Maximal contact and going down 170 3.9. Restriction of derivatives and going up 172 3.10. Uniqueness of maximal contact 178 3.11. Tuning of ideals 183 3.12. Order reduction for ideals 186 3.13. Order reduction for marked ideals 192 Bibliography 197 Index 203

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Book SynopsisModular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. This title gives an algorithm for computing coefficients of modular forms of level one in polynomial time.Trade Review"The book is well written and provides sufficient detail and reminders about the big picture. It gives a nice exposition of the material involved and should be accessible to graduate students or researchers with a sufficient background in number theory and algebraic geometry."--Jeremy A. Rouse, Mathematical Reviews ClippingsTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. ix*Acknowledgments, pg. x*Author information, pg. xi*Dependencies between the chapters, pg. xii*Chapter 1. Introduction, main results, context, pg. 1*Chapter 2. Modular curves, modular forms, lattices, Galois representations, pg. 29*Chapter 3. First description of the algorithms, pg. 69*Chapter 4. Short introduction to heights and Arakelov theory, pg. 79*Chapter 5. Computing complex zeros of polynomials and power series, pg. 95*Chapter 6. Computations with modular forms and Galois representations, pg. 129*Chapter 7. Polynomials for projective representations of level one forms, pg. 159*Chapter 8. Description of X1(5l), pg. 173*Chapter 9. Applying Arakelov theory, pg. 187*Chapter 10. An upper bound for Green functions on Riemann surfaces, pg. 203*Chapter 11. Bounds for Arakelov invariants of modular curves, pg. 217*Chapter 12. Approximating Vf over the complex numbers, pg. 257*Chapter 13. Computing Vf modulo p, pg. 337*Chapter 14. Computing the residual Galois representations, pg. 371*Chapter 15. Computing coefficients of modular forms, pg. 383*Epilogue, pg. 399*Bibliography, pg. 403*Index, pg. 423

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Book SynopsisStudies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. The author also uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula.Trade Review"This book is a research monograph, yet the author takes care in recalling in detail the relevant notation and previous results instead of just referring to the literature. Also, explicit calculations are given, making the book readable not only for experts but also for interested advanced students."--Eva Viehmann, Mathematical ReviewsTable of ContentsPreface vii Chapter 1: The fixed point formula 1 Chapter 2: The groups 31 Chapter 3: Discrete series 47 Chapter 4: Orbital integrals at p 63 Chapter 5: The geometric side of the stable trace formula 79 Chapter 6: Stabilization of the fixed point formula 85 Chapter 7: Applications 99 Chapter 8: The twisted trace formula 119 Chapter 9: The twisted fundamental lemma 157 Appendix: Comparison of two versions of twisted transfer factors 189 Bibliography 207 Index 215

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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 SynopsisOver the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedTrade Review"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215

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Book SynopsisDescent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fTrade Review"An impressive tour de force."--Bertrand Remy, Jahresbericht der DMVTable of ContentsPreface xi PART 1. MOUFANG QUADRANGLES 1 Chapter 1. Buildings 3 Chapter 2. Quadratic Forms 13 Chapter 3. Moufang Polygons 23 Chapter 4. Moufang Quadrangles 31 Chapter 5. Linked Tori, I 41 Chapter 6. Linked Tori, II 47 Chapter 7. Quadratic Forms over a Local Field 57 Chapter 8. Quadratic Forms of Type E6, E7 and E8 69 Chapter 9. Quadratic Forms of Type F4 79 PART 2. RESIDUES IN BRUHAT-TITS BUILDINGS 83 Chapter 10. Residues 85 Chapter 11. Unramified Quadrangles of Type E6, E7 and E8 91 Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 93 Chapter 13. Ramified Quadrangles of Type E6, E7 and E8 101 Chapter 14. Quadrangles of Type E6, E7 and E8: Summary 109 Chapter 15. Totally Wild Quadratic Forms of Type E7 115 Chapter 16. Existence 119 Chapter 17. Quadrangles of Type F4 129 Chapter 18. The Other Bruhat-Tits Buildings 137 PART 3. DESCENT 141 Chapter 19. Coxeter Groups 143 Chapter 20. Tits Indices 153 Chapter 21. Parallel Residues 165 Chapter 22. Fixed Point Buildings 181 Chapter 23. Subbuildings 195 Chapter 24. Moufang Structures 205 Chapter 25. Fixed Apartments 217 Chapter 26. The Standard Metric 221 Chapter 27. Affine Fixed Point Buildings 233 PART 4. GALOIS INVOLUTIONS 241 Chapter 28. Pseudo-Split Buildings 243 Chapter 29. Linear Automorphisms 251 Chapter 30. Strictly Semi-linear Automorphisms 259 Chapter 31. Galois Involutions 271 Chapter 32. Unramified Galois Involutions 275 PART 5. EXCEPTIONAL TITS INDICES 285 Chapter 33. Residually Pseudo-Split Buildings 287 Chapter 34. Forms of Residually Pseudo-Split Buildings 297 Chapter 35. Orthogonal Buildings 303 Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings 309 Bibliography 327 Index 333

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Book SynopsisIn the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the autoTrade Review"This book is beautiful and will be at the origin of many advances in the general theory of arbitrary algebraic groups."--Bertrand Remy, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminary notions, pg. 15*3. Field-theoretic and linear-algebraic invariants, pg. 28*4. Central extensions and groups locally of minimal type, pg. 57*5. Universal smooth k-tame central extension, pg. 66*6. Automorphisms, isomorphisms, and Tits classification, pg. 79*7. Constructions with regular degenerate quadratic forms, pg. 108*8. Constructions when PHI has a double bond, pg. 138*9. Generalization of the standard construction, pg. 171*A. Pseudo-isogenies, pg. 181*B. Clifford constructions, pg. 187*C. Pseudo-split and quasi-split forms, pg. 206*D. Basic exotic groups of type F4 of relative rank 2, pg. 230*Bibliography, pg. 239*Index, pg. 241

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Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Chapter 1. Introduction, pg. 1*Chapter 2. Auxiliary Results, pg. 29*Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet, pg. 50*Chapter 4. Restriction for Surfaces with Linear Height below 2, pg. 57*Chapter 5. Improved Estimates by Means of Airy-Type Analysis, pg. 75*Chapter 6. The Case When hlin(PHI) => 2: Preparatory Results, pg. 105*Chapter 7. How to Go beyond the Case hlin(PHI) => 5, pg. 131*Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4, pg. 181*Chapter 9. Proofs of Propositions 1.7 and 1.17, pg. 244*Bibliography, pg. 251*Index, pg. 257

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a huge range and FREE tracked UK delivery on ALL orders.

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Book Synopsis

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Book Synopsis

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Book Synopsis

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisAlgebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion of algebraic geometry. This book provides a foundation to proceed to advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves.Table of ContentsFundamental concepts The normalization theorem and its applications The Riemann-Roch theorem Applications of the Riemann-Roch theorem Abel's theorem and its applications.

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Book SynopsisIn these volumes, a reader will find all of John Tate's published mathematical papers-spanning more than six decades-enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.Table of Contents Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. Tate A note on finite ring extensions by E. Artin and J. T. Tate On the relation between extremal points of convex sets and homomorphisms of algebras by J. Tate Genus change in inseparable extensions of function fields by J. Tate On Chevalley's proof of Luroth's theorem by S. Lang and J. Tate The higher dimensional cohomology groups of class field theory by J. Tate The cohomology groups of algebraic number fields by J. T. Tate On the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. Tate On the characters of finite groups by R. Brauer and J. Tate Homology of Noetherian rings and local rings by J. Tate WC-groups over $p$-adic fields by J. Tate On the inequality of Castelnuovo-Severi by E. Artin and J. Tate On the inequality of Castelnuovo-Severi, and Hodge's theorem by J. Tate Principal homogeneous spaces over abelian varieties by S. Lang and J. Tate Principal homogeneous spaces for abelian varieties by J. Tate A different with an odd class by A. Frohlich, J.-P. Serre, and J. Tate Nilpotent quotient groups by J. Tate Duality theorems in Galois cohomology over number fields by J. Tate Ramification groups of local fields by S. Sen and J. Tate Formal complex multiplication in local fields by J. Lubin and J. Tate Algebraic cycles and poles of zeta functions by J. T. Tate Elliptic curves and formal groups by J. Lubin, J. Serre, and J. Tate On the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. Tate Formal moduli for one-parameter formal Lie groups by J. Lubin and J. Tate The cohomology groups of tori in finite Galois extensions of number fields by J. Tate Global class field theory by J. T. Tate Endomorphisms of abelian varieties over finite fields by J. Tate The rank of elliptic curves by J. T. Tate and I. R. Safarevic Residues of differentials on curves by J. Tate $p$-divisible groups by J. T. Tate The work of David Mumford by J. Tate Classes d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. Tate Good reduction of abelian varieties by J.-P. Serre and J. Tate Group schemes of prime order by J. Tate and F. Oort Symbols in arithmetic by J. Tate Rigid analytic spaces by J. Tate The Milnor ring of a global field by H. Bass and J. Tate Appendix by H. Bass and J. Tate Letter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. Tate Points of order 13 on elliptic curves by B. Mazur and J. Tate The arithmetic of elliptic curves by J. T. Tate The 1974 Fields Medals (I): An algebraic geometer by J. Tate Algorithm for determining the type of a singular fiber in an elliptic pencil by J. Tate Letters by J. Tate

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Book SynopsisAlgebraic Geometry has been at the centre of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology.

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Book SynopsisProvides the kind of mathematical knowledge and experiences that students will need for courses in other fields, such as biology, chemistry, business, finance, economics, and other areas that are heavily dependent on data either from laboratory experiments or from other studies. The focus is on the fundamental mathematical concepts and realistic problem-solving via mathematical modelling.Trade Review… On initial viewing, “Functions, Data and Models” may seem like a typical textbook, with all the usual key parts, including appendixes and answers to selected problems in the back of the book. However, on closer examination, readers will see and understand how the eight-chapter work differs from classic algebra books. The detailed preface includes messages for the student, messages for the instructor, and information on the book's philosophy. … The book would be a great resource for any algebra course. Highly recommended." - K.D. Holton, CHOICE Magazine"This textbook certainly sets the hook early when authors explain in the preface that the book's philosophy is to allow students to focus on mathematical ideas, not mathematical calculations. … As the authors point out in the introduction to this text, it contains enough material (in both depth and variety) to cover two semesters' worth of study. On the other hand, the interested instructor could easily design a syllabus covering a limited number of topics from the book to address the needs of a semester-long course. I highly recommend this text to instructors who seek to cultivate creativity and critical thinking in their college-algebra-level students" - Hilary Fletcher, Mathematics and Computer EducationTable of Contents Preface 1. Data Everywhere 2. Functions Everywhere 3. Linear Functions 4. More about Linear Functions 5. Families of Nonlinear Functions 6. Polynomial Functions 7. Extended Families of Functions 8. Modeling Periodic Phenomena Appendices Selected Short Answers About the Authors

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Book SynopsisThis book, a translation of the German volume n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra in a form that is easily accessible to the student who lacks a sophisticated background in mathematics. It stimulates geometrical thought by applying the tools of linear algebra and the algebra of polynomials to a concrete geometrical situation to reveal some rather surprising insights into the geometry of n-gons. The twelve chapters treat n-gons, classes of n-gons, and mapping of the set of n-gons into itself. Exercises are included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials.(Mathematical Expositions No. 18)

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Book SynopsisOffers a rigorous and coherent introduction to the five basic number systems of mathematics - natural numbers, integers, rational numbers, real numbers, and complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.Table of Contents Natural numbers Integers Rational numbers Real numbers Complex numbers Sets, relations, functions Bibliography Index

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Book SynopsisTrade ReviewThe book under review contains six chapters that can be read independently, each one surveying one mathematical topic. ... It is carefully written, and it is better than a collection of lecture notes. Such books are needed for students, as a complement to the standard textbooks and to present more specialized applications of classical mathematics. The reviewer wishes there were many more such books." - Athanase Papadopoulos, Zentralblatt MATH"This book has its origins, we are told, in the authors' experiences teaching graduate students in computer science, who needed background in certain mathematical topics. Since these topics were not covered in the basic courses that these students had taken, the authors undertook to introduce them in courses spanning several semesters, the lecture notes of which, suitably expanded, became this text. ... I like expository books, because I think, particularly in these days of increasing specialization, that they serve a valuable purpose, not only for students but also professionals who want to see what's going on in other areas, or who need some background in one area for research in another. This book is a fine example of that genre." - Mark Hunacek, MAA ReviewsTable of Contents Measaure and integral High-dimensional geometry and measure concentration Fourier analysis Representations of finite groups Polynomials Topology Index

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Book SynopsisTrade Review...this book is certainly a must-have for any researcher working in tensor categories or a related field, and is already the standard reference in the subject." - Julien Bichon, AMS BlogsTable of Contents Abelian categories Monoidal categories $\mathbb{Z}_ $-rings Tensor categories Representation categories of Hopf algebras Finite tensor categories Module categories Braided categories Fusion categories Bibliography Index

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Book SynopsisAddresses various aspects of the theory of automorphic forms and its relations with the theory of $L$-functions, the theory of elliptic curves, and representation theory. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to build bridges to mathematical questions in other fields.Table of Contents S. Anni, A note on the minimal level of realization for a mod $\ell$ eigenvalue system A. Arnold-Roksandich, A discussion on the number eta-quotients of prime level C. Burrin, Dedekind sums, reciprocity, and non-arithmetic groups G. Chinta, I. Horozov, and C. O'Sullivan, Noncommutative modular symbols and Eisenstein series A. Espinosa, An annotated discussion of a panel presentation on improving diversity in mathematics J. S. Friedman, J. Jorgenson, and L. Smajlovic, Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps X. Guitart and M. Masdeu, Computing $p$-adic periods of abelian varieties from automorphic forms A. Haensch and B. Kane, An algebraic and analytic approach to spinor exceptional behavior in translated lattices A. K. Jha and B. Sahu, Differential operators on Jacobi forms and special values of certain Dirichlet series J. Jorgenson and L. Smajlovic, Some results in study of Kronecker limit formula and Dedekind sums D. Kelmer, Equidistribution of shears and their arithmetic applications K. Khuri-Makdisi, Fake proofs for identities involving products of Eisenstein series K. Khuri-Makdisi, Modular forms constructed from moduli of elliptic curves, with applications to explicit models of modular curves B. Kumar, J. Meher, and S. Pujahari, Some remarks on the coefficients of symmetric power $L$-functions J. Li, On primes in arithmetic progressions B. Linowitz and L. Thompson, The Fourier coefficients of Eisenstein series newforms K. Maurischat, Properties of Sturm's formula A. Odzak and L. Sceta, An application of a special form of a Tauberian theorem A. Odzak and L. Sceta, On the zeros of some $L$ functions from the extended Selberg class E. Ozman, Rational points on twisted modular curves B. Ramakrishnan, B. Sahu, and A. K. Singh, On the number of representations of certain quadratic forms in 8 variables M. Roy, Level of Siegel modular forms constructed via $\textrm{sym}^3$ lifting F. Stromberg, Dimension formulas and kernel functions for Hilbert modular forms H. Then, An explicit evaluation of the Hauptmoduli at elliptic points for certain arithmetic groups A. Trbovic, Torsion groups of elliptic curves over quadratic fields S. Wagh, Maass space for lifting from SL(2,$\mathbb{R}$) to GL(2,B) over a division quaternion algebra N. Walji, On the occurrence of large positive Hecke eigenvalues for GL(2) L. H. Walling, Representations by quadratic forms and the Eichler Commutation Relation S. Yamana, Degenerate principal series and Langlands classification.

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Book SynopsisExplains the foundations of a version of algebraic geometry in which rings or algebras are replaced by $C^\infty $-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are $C^\infty $-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps.Table of Contents Introduction $C^\infty$-rings The $C^\infty$-ring $C^\infty (X)$ of a manifold $X$ $C^\infty $-ringed spaces and $C^\infty $-schemes Modules over $C^\infty$-rings and $C^\infty $-schemes $C^\infty $-stacks Deligne-Mumford $C^\infty $-stacks Sheaves on Deligne-Mumford $C^\infty $-stacks Orbifold strata of $C^\infty $-stacks Appendix A. Background material on stacks Bibliography Glossary of Notation Index.

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Book SynopsisExplores various topics of universal algebra, universal algebraic geometry, logic geometry, and algebraic logic, as well as applications of universal algebra to computer science, geometric ring theory, small cancellation theory, and Boolean algebras.Table of Contents A. Atkarskaya, A. Kanel-Belov, E. Plotkin, and E. Rips, Construction of a quotient ring of $\mathbb{Z}_f\mathcal{F}$ in which a binomial $(1+w)$ is invertible using small cancellation methods E. Aladova, Geometric view on homogenous groups E. Aladova and T. Plotkin, Syntax versus semantaics in knowledge bases II J. Cirulis, Polyadic algebras with terms: A signature-free approach R. Lipyanski, Geometric equivalence of $\pi$-torsion-free nilpotent groups R. Lipyanski, On the Zariski topology of $\Omega$-groups B. Plotkin, Seven lectures on universal algebraic geometry A. N. Shevlyakov, New problems in universal algebraic geometry illustrated by Boolean equations.

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Book SynopsisContains the proceedings of the Arizona Winter School 2016, held in March 2016 at The University of Arizona. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry.Table of Contents A. C. Cojocaru, Primes, elliptic curves and cyclic groups H. A. Helfgott, Growth and expansion in algebraic groups over finite fields E. Fouvry, E. Kowalski, P. Michel, and W. Sawin, Lectures on applied $\ell$-adic cohomology A. V. Sutherland, Sato-Tate distributions.

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Book SynopsisProvides a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of $m\times m$ matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation.Trade ReviewThe present book is a nice and introductory reference to graduate students or researchers who are working in the field of representation and invariant theory." — Yin Chen, Zentralblatt MATH"The choices made by the authors permit them to highlight the main results and also to keep the material within the reach of an interested reader. At the same time, the book remains open-ended with precise pointers to the literature on other approaches and the cases not treated here." — Felipe Zaldivar, MAA ReviewsTable of Contents Introduction and preliminaries The classical theory Quasi-hereditary algebras The Schur algebra Matrix functions and invariants Relations The Schur algebra of a free algebra Bibliography General index Symbol index.

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Book SynopsisFunctional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, and physics. This book provides a comprehensive introduction to the field for graduate students and researchers. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a course on functional analysis for beginning graduate students.Table of Contents Foundations Principles of functional analysis The weak and weak* topologies Fredholm theory Spectral theory Unbounded operators Semigroups of operators Zorn and Tychonoff Bibliography Notation Index

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Book SynopsisPresents original research articles covering a large range of topics, including weight enumerators for codes, function field analogs of the Brauer-Siegel theorem, the computation of cohomological invariants of curves, the trace distributions of algebraic groups, and applications of the computation of zeta functions of curves.Table of Contents J. D. Achter and E. W. Howe, Hasse-Witt and Cartier-Manin matrices: A warning and a request M. Hindry, Analogues of Brauer-Siegel theorem in arithmetic geometry J. Javanpeykar and J. Voight, The Belyi degree of a curve is computable N. Kaplan, Weight enumerators of Reed-Muller codes from cubic curves and their duals G. Lachaud, The distribution of the trace in the compact group of type $G_2$ B. Malmskog, R. Pries, and C. Weir, The de Rham cohomology of the Suzuki curves F. Pazuki, Decompositions en hauteurs locales B. Poonen, Using zeta functions to factor polynomials over finite fields J. Sijsling, Canonical models of arithmetic $(1;\infty)$-curves A. V. Sutherland and J. F. Voloch, Maps between curves and arithmetic obstructions.

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Book SynopsisIncludes research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables.Table of Contents A. Anastasiou, L. Borsten, M. J. Duff, A. Marrani, S. Nagy, and M. Zoccali, The mile high magic pyramid M. R. Bremner, Symmetrization of Jordan dialgebras J. S. Carter, V. Lebed, and S. Y. Yang, A prismatic classifying space P. Dehornoy, Some aspects of the SD-world A. Drapal, About Laver tables J. Feldvoss, Leibniz algebras as non-associative algebras M. Greer, Simple right conjugacy closed loops B. Im and J. D. H. Smith, Orthogonality of approximate Latin squares and quasigroups S. Mukherjee and J. H. Przytycki, On the rack homology of graphic quandles A. Nowak, Modules over semisymmetric quasigroups J. D. Phillips, Moufang and commutant elements in magmas S. Pumplun, The multiplicative loops of Jha-Johnson semifields A. Romanowska, Convex sets and barycentric algebras I. Stuhl and P. Vojtechovsky, Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order P. Truini, M. Rios, and A. Marrani, The magic star of exceptional periodicity.

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Book SynopsisContains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, in June 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem. The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope.Table of Contents R. Bezrukavnikov and D. Kazhdan, Character values and Hochschild homology A. Braverman and D. Kazhdan, Schwartz space of parabolic basic affine space and asymptotic Hecke algebras C. J. Bushnell and G. Henniart, Explicit local Jacquet-Langlands correspondence: The non-dyadic wild case T.-H. Chen, D. Gaitsgory, and A. Yom Din, On the Casselman-Jacquet functor W. T. Gan, Periods and theta correspondence D. Gourevitch and S. Sahi, Generalized and degenerate Whittaker quotients and Fourier coefficients C. Gruson and V. Serganova, Geometric approach to the fermionic Fock space, via flag varieties and representations of algebraic (super)groups G. Henniart and M.-F. Vigneras, Representations of a $p$-adic group in characteristic $p$ E. Lapid, On the support of matrix coefficients of supercuspidal representations of the general linear group over a local non-archimedean field G. Lusztig, On the generalized Springer correspondence R. Ollivier and P. Schneider, The modular pro-$p$ Iwahori-Hecke Ext-algebra E. Opdam, Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda on the Plancherel density A. Reznikov, Limiting cycles and periods of Maass forms L. Xiao and X. Zhu, On vector-valued twisted conjugation invariant functions on a group with an appendix by Stephen Donkin C.-B. Zhu, Local theta correspondence and nilpotent invariants

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Book Synopsis

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Book Synopsis

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Book Synopsis

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Book SynopsisContains the proceedings of the conference “A Panorama on Singular Varieties”, held in February 2017, at the University of Seville. The articles cover a wide range of topics in the study of singularities and should be of great value to graduate students and research faculty who have a basic background in the theory of singularities.Table of Contents P. Aluffi and M. Goresky, Pfaffian integrals and invariants of singular varieties J. L. Cisneros-Molina and A. Romano-Velazquez, The real embedding method to study mixed functions A. Dimca and G. Sticlaru, Computing Milnor fiber monodromy for some projective hypersurfaces G.-M. Greuel, Straight equisingular deformations and punctual Hilbert schemes H. A. Hamm, Divisor class groups of singular varieties E. Hironaka, The augmented deformation space of rational maps T. Laszlo and A. Nemethi, On the geometry of strongly flat semigroups and their generalizations D. B. Massey, Characteristic cycles and the relative local Euler obstruction L. Narvaez Macarro, Hasse-Schmidt derivations versus classical derivations M. Oka, On the connectivity of Milnor fiber for mixed functions J. E. Sampaio, Some classes of homeomorphisms that preserve multiplicity and tangent cones J.-P. Teyssier, Higher dimensional Stokes structures are rare.

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