{"title":"Algebraic geometry Books","description":"","products":[{"product_id":"a-first-course-in-modular-forms-9780387232294","title":"A First Course in Modular Forms","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves;\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“The textbook under review provides a modern introduction to the theory of modular forms, with the aim to explain the modularity theorem to beginning graduate students and advanced undergraduates. … Written in a very comprehensible, detailed, lucid and instructive manner, this unique textbook is widely self-contained and perfectly suitable for self-study by beginners. … an excellent guide to the relevant research literature … . experts and teachers will get a lot of methodological inspiration from the authors’ approach, and many useful ideas for efficient teaching.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, June, 2013)\u003c\/p\u003e\u003cp\u003e\"It has always been difficult to start learning about modular forms. … we were still lacking a textbook that could be honestly described as both comprehensive and accessible. Diamond and Shurman’s First Course is a largely successful attempt to provide just such a book. … A First Course in Modular Forms is a success. … a course taught from this text would be a very good way to lead students into the area. … I expect that Diamond and Shurman’s book would serve very well.\" (Fernando Q. Gouvêa, MathDL, February, 2007)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"An essentially self-contained treatment that readers will find valuable both as a reference and a pedagogical text. ... The authors of FCMF are to be commended for producing a valuable addition to the literature which belongs on the shelf of all scholars with an interest in modular forms, modular curves and their arithmetic applications.\" (Henri Darmon, Mathematical Reviews, Issue 2006 f)\u003c\/p\u003e\u003cp\u003e\"The aim of this book is to introduce the reader to the modularity theorem. … This book can be recommended to everyone wishing to learn about modular forms and their connections to number theory.\" (J. Mahnkopf, Monatshefte für Mathematik, Vol. 146 (4), 2006)\u003c\/p\u003e\u003cp\u003e\"The … goal of Diamond (Brandeis Univ.) and Shurman (Reed College) is … to state the modularity conjecture in some of its many forms. … readers wishing eventually to read Wiles could hardly find a better place to start than this. … Summing Up: Highly recommended. General readers; upper-division undergraduates through professionals.\" (D. V. Feldman, CHOICE, Vol. 43 (1), September, 2005)\u003c\/p\u003e\u003cp\u003e\"The textbook under review provides a modern introduction to the theory of modular forms … . This ambitious program … is carried out in as down-to-earth a way as possible. … this is the first comprehensive introduction to the recent modularity theorem … . Written in a very comprehensible, detailed, lucid and instructive manner, this unique textbook is widely self-contained and perfectly suitable for self-study by beginners. Moreover, this book is an excellent guide to the relevant research literature … .\" (Werner Kleinert, Zentralblatt MATH, Vol. 1062 (13), 2005)\u003c\/p\u003e\u003cp\u003e\"While there are many books on modular forms and elliptic curves, and some of them discuss the Eicheler-Shimura theory, most that describe it do not go deeply into the proofs. … The book of Diamond and Shurman addresses this need. … it is clearly directed to the serious student and it will unquestionably be a useful book even to experts. … this is a very unique and valuable book, and one that I would recommend to anyone wishing to learn about modular forms … .\" (Daniel Bump, SIAM Review, Vol. 47 (4), 2005)\u003c\/p\u003e\u003cp\u003e\"This introduction to modular forms is aimed at students with only a basic knowledge of complex function theory. … A useful and up-to-date exposition of topics scattered throughout the literature, aided by exercises with answers.\" (Mathematika, Vol. 52, 2005)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eModular Forms, Elliptic Curves, and Modular Curves.- Modular Curves as Riemann Surfaces.- Dimension Formulas.- Eisenstein Series.- Hecke Operators.- Jacobians and Abelian Varieties.- Modular Curves as Algebraic Curves.- The Eichler-Shimura Relation and L-functions.- Galois Representations.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733725557079,"sku":"9780387232294","price":43.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387232294.jpg?v=1720001397"},{"product_id":"algebraic-groups-and-number-theory-volume-1-9780521113618","title":"Algebraic Groups and Number Theory Volume 1","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is the first volume of a two-volume book that offers an in-depth, and essentially self-contained, treatment of the arithmetic theory of algebraic groups. It is accessible to graduate students and researchers in number theory, algebraic geometry, and related areas.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'The original English version of the book 'Algebraic Groups and Number Theory' by Platonov and Rapinchuk was a go to reference for graduate students and senior researchers alike working in areas of arithmetic and algebraic groups, discrete subgroups of Lie groups, and connections with number theory. The second edition, which will be split into two volumes, and also co-authored with I. Rapinchuk, is a welcome and timely update to the original. The first volume of the second edition, consists of an update to chapters 1-5 of the original with an additional section 4.9 to include new material on the structure of extensions of arithmetic groups. There is no doubt in my mind that this first volume of the second edition will again take on the role of a go to text for those working in an area of huge ongoing interest and importance, and be at the forefront training new generations of mathematicians working in the areas of arithmetic and algebraic groups, discrete subgroups of Lie groups, and connections with number theory.' Alan Reid, Rice University\u003cbr\u003e'The arithmetic theory of algebraic groups is a beautiful area of mathematics: a crossroad of number theory, groups, geometry, representation theory, and more. Not surprisingly it attracted some of the greatest mathematicians of the last few generations. The first edition of the book 'Algebraic Groups and Number Theory' by Vladimir Platonov and Andrei Rapinchuk which came out in the early 90s has quickly become the standard reference of the field. It presents in a clear way several deep topics. The book was one of the reasons the area attracted more researchers and expanded to new directions. This made an updated version much needed. The original authors and Igor Rapinchuk should be thanked by the mathematical community for carrying out this monumental job.' Alex Lubotzky, Hebrew University of Jerusalem\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Algebraic number theory; 2. Algebraic groups; 3. Algebraic groups over locally compact fields; 4. Arithmetic groups and reduction theory; 5. Adeles; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48733845225815,"sku":"9780521113618","price":52.24,"currency_code":"GBP","in_stock":true}]},{"product_id":"complex-algebraic-threefolds-9781108844239","title":"Complex Algebraic Threefolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe first book on the explicit birational geometry of complex algebraic threefolds, this detailed text covers all the knowledge of threefolds needed to enter the field of higher dimensional birational geometry. Containing over 100 examples and many recent results, it is suitable for advanced graduate students as well as researchers.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'This book is an excellent introduction to the classification of complex algebraic threefolds. It includes a thorough modern treatment and a glimpse into many of the recent higher dimensional breakthroughs.' Christopher Hacon, University of Utah\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. The minimal model program; 2. Singularities; 3. Divisorial contractions to points; 4. Divisorial contractions to curves; 5. Flips; 6. The Sarkisov category; 7. Conical fibrations; 8. Del Pezzo fibrations; 9. Fano threefolds; 10. Minimal models; References; Notation; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738344403287,"sku":"9781108844239","price":66.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"introduction-to-algebraic-geometry-9783030626433","title":"Introduction to Algebraic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. \u003cbr\u003e\u003cbr\u003eThe text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The prerequisites to read this book are undergraduate analysis, algebra and topology. The proofs of all needed more advanced results of topology or algebra are given. The book is mainly self-contained; some proofs with all the necessary steps are proposed as exercises. … Each chapter ends with a set of exercises.” (Jean-Marc Drézet's, Mathematical Reviews, June, 2022)\u003cbr\u003e\u003cbr\u003e“The present book is a very solid, and different than usual (or traditional), introduction to algebraic geometry that we can find on the market. … I can honestly recommend this item as a main reference for (advanced) courses devoted to algebraic geometry, and for extended courses devoted to introduction to algebraic geometry – this claim is based on the fact that the book is self-contained on the level of commutative algebra and due to this reason provides a coherent narration.” (Piotr Pokora, zbMATH 1471.14003, 2021)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Introduction.- Beginning concepts.- Schemes.- Properties of schemes.- Sheaves of modules.- Introduction to Cohomology.- Cohomology in algebraic geometry.- Exercises.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743042875735,"sku":"9783030626433","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030626433.jpg?v=1720063860"},{"product_id":"drinfeld-modules-9783031197062","title":"Drinfeld Modules","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory.\u003cbr\u003eAfter the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized.\u003cbr\u003e\u003ci\u003eDrinfeld Modules\u003c\/i\u003e guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Acknowledgements.- Notation and Conventions.- Chapter 1. Algebraic Preliminaries.- Chapter 2. Non-Archimedean Fields.- Chapter 3. Basic Properties of Drinfeld Modules.- Chapter 4. Drinfeld Modules over Finite Fields.- Chapter 5. Analytic Theory of Drinfeld Modules.- Chapter 6. Drinfeld Modules over Local Fields.- Chapter 7. Drinfeld Modules over Global Fields.- Appendix A. Drinfeld modules for general function rings.- Appendix B. Notes on exercises.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743075086679,"sku":"9783031197062","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031197062.jpg?v=1720064000"},{"product_id":"abelian-varieties-over-the-complex-numbers-a-graduate-course-9783031255694","title":"Abelian Varieties over the Complex Numbers: A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.\u003cbr\u003eThe book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier–Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained.\u003cbr\u003eThis book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The reorganization of the topics is fine surgical work. Several portions of the original monograph are sewn in a natural way in the new book, adding examples or additional text when necessary, and re-arranging the focus to make it a more friendly introduction to the subject. Careful attention to details and the required background makes the book under review accessible to an interested reader and could be a used as textbook for a course on abelian varieties.” (Felipe Zaldivar, MAA Reviews, June 18, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Line Bundles on Complex Tori.- 2 Abelian Varieties.- 3 Moduli Spaces.- 4 Jacobian Varieties.- 5 Main Examples of Abelian Varieties.- 6 The Fourier Transform for Sheaves and Cycles.- 7 Introduction to the Hodge Conjecture for Abelian Varieties.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743077052759,"sku":"9783031255694","price":39.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031255694.jpg?v=1720064009"},{"product_id":"elements-de-geometrie-rigide-volume-i-construction-et-etude-geometrique-des-espaces-rigides-9783034800112","title":"Éléments de Géométrie Rigide: Volume I.","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eLa géométrie rigide est devenue, au fil des ans, un outil indispensable dans un grand nombre de questions en géométrie arithmétique. Depuis ses premières fondations, posées par J. Tate en 1961, la théorie s'est développée dans des directions variées. Ce livre est le premier volume d'un traité qui expose un développement systématique de la géométrie rigide suivant l'approche de M. Raynaud, basée sur les schémas formels à éclatements admissibles près. Ce volume est consacré à la construction des espaces rigides dans une situation relative et à l'étude de leurs propriétés géométriques. L'accent est particulièrement mis sur l'étude de la topologie admissible d'un espace rigide cohérent, analogue de la topologie de Zariski d'un schéma. Parmi les sujets traités figurent l'étude des faisceaux cohérents et de leur cohomologie, le théorème de platification par éclatements admissibles qui généralise au cadre formel-rigide un théorème de Raynaud-Gruson dans le cadre algébrique, et le théorème de comparaison du type GAGA pour les faisceaux cohérents. Ce volume contient aussi de larges rappels et compléments de la théorie des schémas formels de Grothendieck. Ce traité est destiné tout autant aux étudiants ayant une bonne connaissance de la géométrie algébrique et souhaitant apprendre la géométrie rigide qu'aux experts en géométrie algébrique et en théorie des nombres comme source de références. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePréface par Michel Raynaud.- Avant-propos.- Introduction.- Chapitre 1. Préliminaires.- Chapitre 2. Géométrie formelle.- Chapitre 3. Éclatements admissibles.- Chapitre 4. Géométrie rigide.- Chapitre 5. Platitude.- Chapitre 6. Invariants différentiels. Morphismes lisses.- Chapitre 7. Espaces rigides quasi-séparés.- Bibliographie.- Index.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743087309143,"sku":"9783034800112","price":94.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783034800112.jpg?v=1720064055"},{"product_id":"differential-geometry-connections-curvature-and-characteristic-classes-9783319550824","title":"Differential Geometry: Connections, Curvature,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of  de Rham cohomology is required for the last third of the text.\u003cp\u003ePrerequisite material is contained in author's text \u003ci\u003eAn Introduction to Manifolds\u003c\/i\u003e, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included.\u003c\/p\u003e\u003cp\u003eDifferential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields.  The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The textbook is a concise and well organized treatment of characteristic classes on principal bundles. It is characterized by a right balance between rigor and simplicity. It should be in every mathematician's arsenal and take its place in any mathematical library.” (Nabil L. Youssef, zbMATH 1383.53001, 2018)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Chapter 1. Curvature and Vector Fields.- 1. Riemannian Manifolds.- 2. Curves.- 3. Surfaces in Space.- 4. Directional Derivative in Euclidean Space.- 5. The Shape Operator.- 6. Affine Connections.- 7. Vector Bundles.- 8. Gauss's Theorema Egregium.- 9. Generalizations to Hypersurfaces in Rn+1.- Chapter 2. Curvature and Differential Forms.- 10. Connections on a Vector Bundle.- 11. Connection, Curvature, and Torsion Forms.- 12. The Theorema Egregium Using Forms.- Chapter 3. Geodesics.- 13. More on Affine Connections.- 14. Geodesics.- 15. Exponential Maps.- 16. Distance and Volume.- 17. The Gauss-Bonnet Theorem.- Chapter 4. Tools from Algebra and Topology.- 18. The Tensor Product and the Dual Module.- 19. The Exterior Power.- 20. Operations on Vector Bundles.- 21. Vector-Valued Forms.- Chapter 5. Vector Bundles and Characteristic Classes.- 22. Connections and Curvature Again.- 23. Characteristic Classes.- 24. Pontrjagin Classes.- 25. The Euler Class and Chern Classes.- 26. Some Applications of Characteristic Classes.- Chapter 6. Principal Bundles and Characteristic Classes.- 27. Principal Bundles.- 28. Connections on a Principal Bundle.- 29. Horizontal Distributions on a Frame Bundle.- 30. Curvature on a Principal Bundle.- 31. Covariant Derivative on a Principal Bundle.- 32. Character Classes of Principal Bundles.- A. Manifolds.- B. Invariant Polynomials.- Hints and Solutions to Selected End-of-Section Problems.- List of Notations.- References.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743098351959,"sku":"9783319550824","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"complex-analytic-desingularization-9784431702184","title":"Complex Analytic Desingularization","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e[From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near “worst” singular points of a complex analytic space obtained by successive “permissible” blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka’s ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry.\u003cbr\u003eIn addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePrologue.- 1 Complex-Analytic Spaces and Elements.- 2 The Weierstrass Preparation Theorem and Its Consequences.- 3 Maximal Contact.- 4 Groves and Polygroves.- 5 The Induction Process.- Epilogue: Singularities of differential equations.- Bibliography.- Index.","brand":"Springer Verlag, Japan","offers":[{"title":"Default Title","offer_id":48743178469719,"sku":"9784431702184","price":104.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"sets-groups-and-mappings-an-introduction-to-abstract-mathematics-9781470449322","title":"Sets Groups and Mappings  An Introduction to","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntroduces the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students who are looking for an entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eLogic and proofs\u003c\/li\u003e\n\u003cli\u003eAn introduction to sets\u003c\/li\u003e\n\u003cli\u003eThe integers\u003c\/li\u003e\n\u003cli\u003eMappings and relations\u003c\/li\u003e\n\u003cli\u003eInduction and recursion\u003c\/li\u003e\n\u003cli\u003eBinary operations\u003c\/li\u003e\n\u003cli\u003eGroups\u003c\/li\u003e\n\u003cli\u003eDivisibility and congruences\u003c\/li\u003e\n\u003cli\u003ePrimes\u003c\/li\u003e\n\u003cli\u003eMultiplicative inverses of residue classes\u003c\/li\u003e\n\u003cli\u003eLinear transformations\u003c\/li\u003e\n\u003cli\u003eIsomorphism\u003c\/li\u003e\n\u003cli\u003eThe symmetric group\u003c\/li\u003e\n\u003cli\u003eExamples of finite groups\u003c\/li\u003e\n\u003cli\u003eCosets\u003c\/li\u003e\n\u003cli\u003eHomomorphisms\u003c\/li\u003e\n\u003cli\u003eGroup actions\u003c\/li\u003e\n\u003cli\u003eEuclidean geometry\u003c\/li\u003e\n\u003cli\u003eEuler's formula\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003cli\u003e\u003cul\u003e\u003c\/ul\u003e\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":48867166388567,"sku":"9781470449322","price":71.1,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470449322.jpg?v=1722281996"},{"product_id":"visual-group-theory-9781470464332","title":"Visual Group Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe more than 300 illustrations in \u003cem\u003eVisual Group Theory\u003c\/em\u003e bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups to advanced structural concepts.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eCarter presents the group theory portion of abstract algebra in a way that allows students to actually see, using a multitude of examples and applications, the basic concepts of group theory … The numerous images (more than 300) are the heart of the text. As this work enables readers to see, experiment with, and understand the significance of groups, they will accumulate examples of groups and their properties that will serve them well in future endeavors in mathematics. Recommended.- J. T. Zerger, \u003ci\u003eChoice\u003c\/i\u003e;\u003cbr\u003e\u003cbr\u003e\"\"If you teach abstract algebra, then this book should be a part of the resources you use. While the phrase “visual abstract algebra” may seem to be a contradiction, the diagrams in this book are an existence proof to the contrary. They are clear, colorful and concise, very easy to understand and sure to aid the students that have difficulty in internalizing the abstract nature of the subject matter …\"\"- Charles Ashbacher, \u003ci\u003eJournal of Recreational Mathematics\u003c\/i\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":48867166585175,"sku":"9781470464332","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"handbook-for-mirror-symmetry-of-calabi-yau-and-fano-manifolds-9781571463890","title":"Handbook for Mirror Symmetry of Calabi–Yau and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn algebraic geometry and theoretical physics, mirror symmetry refers to the relationship between two Calabi–Yau manifolds which appear very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.\u003cbr\u003e\u003cbr\u003eMathematicians became interested in mirror symmetry around 1990, when it was shown that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a long-standing problem.\u003cbr\u003e\u003cbr\u003eToday, mirror symmetry is a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theory, the formalism that physicists use to describe elementary particles. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.\u003cbr\u003e\u003cbr\u003eThis handbook surveys recent developments in mirror symmetry. It presents papers based on selected lectures given at a 2014 Taipei conference on “Calabi–Yau Geometry and Mirror Symmetry,” along with other contributions from invited authors.","brand":"International Press of Boston Inc","offers":[{"title":"Default Title","offer_id":48886391374167,"sku":"9781571463890","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781571463890.jpg?v=1722539873"},{"product_id":"introduction-to-algebraic-geometry-9781470435189","title":"Introduction to Algebraic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePresents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eA crash course in commutative algebra\u003c\/li\u003e\n\u003cli\u003eAffine varieties\u003c\/li\u003e\n\u003cli\u003eProjective varieties\u003c\/li\u003e\n\u003cli\u003eRegular and rational maps of quasi-projective varieties\u003c\/li\u003e\n\u003cli\u003eProducts\u003c\/li\u003e\n\u003cli\u003eThe blow-up of an ideal\u003c\/li\u003e\n\u003cli\u003eFinite maps of quasi-projective varieties\u003c\/li\u003e\n\u003cli\u003eDimension of quasi-projective algebraic sets\u003c\/li\u003e\n\u003cli\u003eZariski's main theorem\u003c\/li\u003e\n\u003cli\u003eNonsingularity\u003c\/li\u003e\n\u003cli\u003eSheaves\u003c\/li\u003e\n\u003cli\u003eApplications to regular and rational maps\u003c\/li\u003e\n\u003cli\u003eDivisors\u003c\/li\u003e\n\u003cli\u003eDifferential forms and the canonical divisor\u003c\/li\u003e\n\u003cli\u003eSchemes\u003c\/li\u003e\n\u003cli\u003eThe degree of a projective variety\u003c\/li\u003e\n\u003cli\u003eCohomology\u003c\/li\u003e\n\u003cli\u003eCurves\u003c\/li\u003e\n\u003cli\u003eAn introduction to intersection theory\u003c\/li\u003e\n\u003cli\u003eSurfaces\u003c\/li\u003e\n\u003cli\u003eRamification and etale maps\u003c\/li\u003e\n\u003cli\u003eBertini's theorem and general fibers of maps\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex.\u003c\/li\u003e\n\u003cli\u003e\u003cul\u003e\u003c\/ul\u003e\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":49083991818583,"sku":"9781470435189","price":110.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470435189.jpg?v=1725550694"},{"product_id":"automorphic-forms-and-related-topics-9781470435257","title":"Automorphic Forms and Related Topics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAddresses 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eS. Anni, A note on the minimal level of realization for a mod $\\ell$ eigenvalue system\u003c\/li\u003e\n\u003cli\u003eA. Arnold-Roksandich, A discussion on the number eta-quotients of prime level\u003c\/li\u003e\n\u003cli\u003eC. Burrin, Dedekind sums, reciprocity, and non-arithmetic groups\u003c\/li\u003e\n\u003cli\u003eG. Chinta, I. Horozov, and C. O'Sullivan, Noncommutative modular symbols and Eisenstein series\u003c\/li\u003e\n\u003cli\u003eA. Espinosa, An annotated discussion of a panel presentation on improving diversity in mathematics\u003c\/li\u003e\n\u003cli\u003eJ. S. Friedman, J. Jorgenson, and L. Smajlovic, Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps\u003c\/li\u003e\n\u003cli\u003eX. Guitart and M. Masdeu, Computing $p$-adic periods of abelian varieties from automorphic forms\u003c\/li\u003e\n\u003cli\u003eA. Haensch and B. Kane, An algebraic and analytic approach to spinor exceptional behavior in translated lattices\u003c\/li\u003e\n\u003cli\u003eA. K. Jha and B. Sahu, Differential operators on Jacobi forms and special values of certain Dirichlet series\u003c\/li\u003e\n\u003cli\u003eJ. Jorgenson and L. Smajlovic, Some results in study of Kronecker limit formula and Dedekind sums\u003c\/li\u003e\n\u003cli\u003eD. Kelmer, Equidistribution of shears and their arithmetic applications\u003c\/li\u003e\n\u003cli\u003eK. Khuri-Makdisi, Fake proofs for identities involving products of Eisenstein series\u003c\/li\u003e\n\u003cli\u003eK. Khuri-Makdisi, Modular forms constructed from moduli of elliptic curves, with applications to explicit models of modular curves\u003c\/li\u003e\n\u003cli\u003eB. Kumar, J. Meher, and S. Pujahari, Some remarks on the coefficients of symmetric power $L$-functions\u003c\/li\u003e\n\u003cli\u003eJ. Li, On primes in arithmetic progressions\u003c\/li\u003e\n\u003cli\u003eB. Linowitz and L. Thompson, The Fourier coefficients of Eisenstein series newforms\u003c\/li\u003e\n\u003cli\u003eK. Maurischat, Properties of Sturm's formula\u003c\/li\u003e\n\u003cli\u003eA. Odzak and L. Sceta, An application of a special form of a Tauberian theorem\u003c\/li\u003e\n\u003cli\u003eA. Odzak and L. Sceta, On the zeros of some $L$ functions from the extended Selberg class\u003c\/li\u003e\n\u003cli\u003eE. Ozman, Rational points on twisted modular curves\u003c\/li\u003e\n\u003cli\u003eB. Ramakrishnan, B. Sahu, and A. K. Singh, On the number of representations of certain quadratic forms in 8 variables\u003c\/li\u003e\n\u003cli\u003eM. Roy, Level of Siegel modular forms constructed via $\\textrm{sym}^3$ lifting\u003c\/li\u003e\n\u003cli\u003eF. Stromberg, Dimension formulas and kernel functions for Hilbert modular forms\u003c\/li\u003e\n\u003cli\u003eH. Then, An explicit evaluation of the Hauptmoduli at elliptic points for certain arithmetic groups\u003c\/li\u003e\n\u003cli\u003eA. Trbovic, Torsion groups of elliptic curves over quadratic fields\u003c\/li\u003e\n\u003cli\u003eS. Wagh, Maass space for lifting from SL(2,$\\mathbb{R}$) to GL(2,B) over a division quaternion algebra\u003c\/li\u003e\n\u003cli\u003eN. Walji, On the occurrence of large positive Hecke eigenvalues for GL(2)\u003c\/li\u003e\n\u003cli\u003eL. H. Walling, Representations by quadratic forms and the Eichler Commutation Relation\u003c\/li\u003e\n\u003cli\u003eS. Yamana, Degenerate principal series and Langlands classification.\u003c\/li\u003e\n\u003cli\u003e\u003cul\u003e\u003c\/ul\u003e\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":49083992080727,"sku":"9781470435257","price":102.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470435257.jpg?v=1725550696"},{"product_id":"algebraic-geometry-ii-9789380250809","title":"Algebraic Geometry II","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSeveral generations of students of algebraic geometry have learned the subject from David Mumford's fabled \"Red Book\" containing notes of his lectures at Harvard University. Their genesis and evolution are described in the preface as:\u003cbr\u003e\u003cbr\u003e\u003cem\u003eInitially notes to the course were mimeographed and bound and sold by the Harvard math department with a red cover. These old notes were picked up by Springer and are now sold as the \"Red book of Varieties and Schemes\". However, every time I taught the course, the content changed and grew. I had aimed to eventually publish more polished notes in three volumes...\u003c\/em\u003e\u003cbr\u003e\u003cbr\u003eThis book contains what Mumford had then intended to be Volume II. It covers the material in the \"Red Book\" in more depth with several more topics added. The notes have been brought to the present form in collaboration with T. Oda.","brand":"Hindustan Book Agency","offers":[{"title":"Default Title","offer_id":49084910010711,"sku":"9789380250809","price":60.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789380250809.jpg?v=1725553714"},{"product_id":"a-primer-on-mapping-class-groups-9780691147949","title":"A Primer on Mapping Class Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe study of the mapping class group Mod(S) is a classical topic that experiences a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"It is clear that a lot of care has been taken in the production of this book, something that indicates the authors' love for the subject. This book should now become the standard text for the subject.\"--Stephen P Humphries, Mathematical Reviews \"[T]his is a very pleasant and appealing book and it is an excellent reference for any reader willing to learn about this fascinating part of mathematics.\"--Raquel Diaz, Alvaro Martinez, European Mathematical Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*Acknowledgments, pg. xiii*Overview, pg. 1*Chapter One. Curves, Surfaces, and Hyperbolic Geometry, pg. 17*Chapter Two. Mapping Class Group Basics, pg. 44*Chapter Three. Dehn Twists, pg. 64*Chapter Four. Generating The Mapping Class Group, pg. 89*Chapter Five. Presentations And Low-Dimensional Homology, pg. 116*Chapter Six. The Symplectic Representation and the Torelli Group, pg. 162*Chapter Seven. Torsion, pg. 200*Chapter Eight. The Dehn-Nielsen-Baer Theorem, pg. 219*Chapter Nine. Braid Groups, pg. 239*Chapter Ten. Teichmuller Space, pg. 263*Chapter Eleven. Teichmuller Geometry, pg. 294*Chapter Twelve. Moduli Space, pg. 342*Chapter Thirteen. The Nielsen-Thurston Classification, pg. 367*Chapter Fourteen. Pseudo-Anosov Theory, pg. 390*Chapter Fifteen. Thurston'S Proof, pg. 424*Bibliography, pg. 447*Index, pg. 465","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49371743715671,"sku":"9780691147949","price":69.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691147949.jpg?v=1730154381"},{"product_id":"first-course-in-algebraic-geometry-and-algebraic-varieties-a-9781800612747","title":"First Course In Algebraic Geometry And Algebraic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties', whose natural continuation is a more advanced course on the theory of schemes, vector bundles, and sheaf-cohomology.Valuable to students studying Algebraic Geometry and Geometry, this title contains around 60 exercises (with solutions) to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full detail. Many examples are discussed in order to reinforce the understanding of both the theoretical elements and their consequences, as well as the possible applications of the material.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":49372533883223,"sku":"9781800612747","price":52.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781800612747.jpg?v=1730163330"},{"product_id":"understanding-geometric-algebr-9780470941638","title":"Understanding Geometric Algebr","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides 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     .\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"This book will benefit scientists and engineers who use electromagnetic theory in the course of their work.”  (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 1 May 2013)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePreface xi\u003c\/b\u003e  \u003cp\u003e\u003cb\u003eReading Guide xv\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. A Quick Tour of Geometric Algebra 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Basic Rules of a Geometric Algebra 16\u003c\/p\u003e \u003cp\u003e2.2 3D Geometric Algebra 17\u003c\/p\u003e \u003cp\u003e2.3 Developing the Rules 19\u003c\/p\u003e \u003cp\u003e2.3.1 General Rules 20\u003c\/p\u003e \u003cp\u003e2.3.2 3D 21\u003c\/p\u003e \u003cp\u003e2.3.3 The Geometric Interpretation of Inner and Outer Products 22\u003c\/p\u003e \u003cp\u003e2.4 Comparison with Traditional 3D Tools 24\u003c\/p\u003e \u003cp\u003e2.5 New Possibilities 24\u003c\/p\u003e \u003cp\u003e2.6 Exercises 26\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Applying the Abstraction 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Space and Time 27\u003c\/p\u003e \u003cp\u003e3.2 Electromagnetics 28\u003c\/p\u003e \u003cp\u003e3.2.1 The Electromagnetic Field 28\u003c\/p\u003e \u003cp\u003e3.2.2 Electric and Magnetic Dipoles 30\u003c\/p\u003e \u003cp\u003e3.3 The Vector Derivative 32\u003c\/p\u003e \u003cp\u003e3.4 The Integral Equations 34\u003c\/p\u003e \u003cp\u003e3.5 The Role of the Dual 36\u003c\/p\u003e \u003cp\u003e3.6 Exercises 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Generalization 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Homogeneous and Inhomogeneous Multivectors 40\u003c\/p\u003e \u003cp\u003e4.2 Blades 40\u003c\/p\u003e \u003cp\u003e4.3 Reversal 42\u003c\/p\u003e \u003cp\u003e4.4 Maximum Grade 43\u003c\/p\u003e \u003cp\u003e4.5 Inner and Outer Products Involving a Multivector 44\u003c\/p\u003e \u003cp\u003e4.6 Inner and Outer Products between Higher Grades 48\u003c\/p\u003e \u003cp\u003e4.7 Summary So Far 50\u003c\/p\u003e \u003cp\u003e4.8 Exercises 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. (3\u003c\/b\u003e+\u003cb\u003e1)D Electromagnetics 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Lorentz Force 55\u003c\/p\u003e \u003cp\u003e5.2 Maxwell’s Equations in Free Space 56\u003c\/p\u003e \u003cp\u003e5.3 Simplifi ed Equations 59\u003c\/p\u003e \u003cp\u003e5.4 The Connection between the Electric and Magnetic Fields 60\u003c\/p\u003e \u003cp\u003e5.5 Plane Electromagnetic Waves 64\u003c\/p\u003e \u003cp\u003e5.6 Charge Conservation 68\u003c\/p\u003e \u003cp\u003e5.7 Multivector Potential 69\u003c\/p\u003e \u003cp\u003e5.7.1 The Potential of a Moving Charge 70\u003c\/p\u003e \u003cp\u003e5.8 Energy and Momentum 76\u003c\/p\u003e \u003cp\u003e5.9 Maxwell’s Equations in Polarizable Media 78\u003c\/p\u003e \u003cp\u003e5.9.1 Boundary Conditions at an Interface 84\u003c\/p\u003e \u003cp\u003e5.10 Exercises 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Review of (3\u003c\/b\u003e+\u003cb\u003e1)D 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Introducing Spacetime 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Background and Key Concepts 98\u003c\/p\u003e \u003cp\u003e7.2 Time as a Vector 102\u003c\/p\u003e \u003cp\u003e7.3 The Spacetime Basis Elements 104\u003c\/p\u003e \u003cp\u003e7.3.1 Spatial and Temporal Vectors 106\u003c\/p\u003e \u003cp\u003e7.4 Basic Operations 109\u003c\/p\u003e \u003cp\u003e7.5 Velocity 111\u003c\/p\u003e \u003cp\u003e7.6 Different Basis Vectors and Frames 112\u003c\/p\u003e \u003cp\u003e7.7 Events and Histories 115\u003c\/p\u003e \u003cp\u003e7.7.1 Events 115\u003c\/p\u003e \u003cp\u003e7.7.2 Histories 115\u003c\/p\u003e \u003cp\u003e7.7.3 Straight-Line Histories and Their Time Vectors 116\u003c\/p\u003e \u003cp\u003e7.7.4 Arbitrary Histories 119\u003c\/p\u003e \u003cp\u003e7.8 The Spacetime Form of ∇ 121\u003c\/p\u003e \u003cp\u003e7.9 Working with Vector Differentiation 123\u003c\/p\u003e \u003cp\u003e7.10 Working without Basis Vectors 124\u003c\/p\u003e \u003cp\u003e7.11 Classifi cation of Spacetime Vectors and Bivectors 126\u003c\/p\u003e \u003cp\u003e7.12 Exercises 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Relating Spacetime to (3\u003c\/b\u003e+\u003cb\u003e1)D 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Correspondence between the Elements 129\u003c\/p\u003e \u003cp\u003e8.1.1 The Even Elements of Spacetime 130\u003c\/p\u003e \u003cp\u003e8.1.2 The Odd Elements of Spacetime 131\u003c\/p\u003e \u003cp\u003e8.1.3 From (3+1)D to Spacetime 132\u003c\/p\u003e \u003cp\u003e8.2 Translations in General 133\u003c\/p\u003e \u003cp\u003e8.2.1 Vectors 133\u003c\/p\u003e \u003cp\u003e8.2.2 Bivectors 135\u003c\/p\u003e \u003cp\u003e8.2.3 Trivectors 136\u003c\/p\u003e \u003cp\u003e8.3 Introduction to Spacetime Splits 137\u003c\/p\u003e \u003cp\u003e8.4 Some Important Spacetime Splits 140\u003c\/p\u003e \u003cp\u003e8.4.1 Time 140\u003c\/p\u003e \u003cp\u003e8.4.2 Velocity 141\u003c\/p\u003e \u003cp\u003e8.4.3 Vector Derivatives 142\u003c\/p\u003e \u003cp\u003e8.4.4 Vector Derivatives of General Multivectors 144\u003c\/p\u003e \u003cp\u003e8.5 What Next? 144\u003c\/p\u003e \u003cp\u003e8.6 Exercises 145\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Change of Basis Vectors 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Linear Transformations 147\u003c\/p\u003e \u003cp\u003e9.2 Relationship to Geometric Algebras 149\u003c\/p\u003e \u003cp\u003e9.3 Implementing Spatial Rotations and the Lorentz Transformation 150\u003c\/p\u003e \u003cp\u003e9.4 Lorentz Transformation of the Basis Vectors 153\u003c\/p\u003e \u003cp\u003e9.5 Lorentz Transformation of the Basis Bivectors 155\u003c\/p\u003e \u003cp\u003e9.6 Transformation of the Unit Scalar and Pseudoscalar 156\u003c\/p\u003e \u003cp\u003e9.7 Reverse Lorentz Transformation 156\u003c\/p\u003e \u003cp\u003e9.8 The Lorentz Transformation with Vectors in Component Form 158\u003c\/p\u003e \u003cp\u003e9.8.1 Transformation of a Vector versus a Transformation of Basis 158\u003c\/p\u003e \u003cp\u003e9.8.2 Transformation of Basis for Any Given Vector 162\u003c\/p\u003e \u003cp\u003e9.9 Dilations 165\u003c\/p\u003e \u003cp\u003e9.10 Exercises 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Further Spacetime Concepts 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Review of Frames and Time Vectors 169\u003c\/p\u003e \u003cp\u003e10.2 Frames in General 171\u003c\/p\u003e \u003cp\u003e10.3 Maps and Grids 173\u003c\/p\u003e \u003cp\u003e10.4 Proper Time 175\u003c\/p\u003e \u003cp\u003e10.5 Proper Velocity 176\u003c\/p\u003e \u003cp\u003e10.6 Relative Vectors and Paravectors 178\u003c\/p\u003e \u003cp\u003e10.6.1 Geometric Interpretation of the Spacetime Split 179\u003c\/p\u003e \u003cp\u003e10.6.2 Relative Basis Vectors 183\u003c\/p\u003e \u003cp\u003e10.6.3 Evaluating Relative Vectors 185\u003c\/p\u003e \u003cp\u003e10.6.4 Relative Vectors Involving Parameters 188\u003c\/p\u003e \u003cp\u003e10.6.5 Transforming Relative Vectors and Paravectors to a Different Frame 190\u003c\/p\u003e \u003cp\u003e10.7 Frame-Dependent versus Frame-Independent Scalars 192\u003c\/p\u003e \u003cp\u003e10.8 Change of Basis for Any Object in Component Form 194\u003c\/p\u003e \u003cp\u003e10.9 Velocity as Seen in Different Frames 196\u003c\/p\u003e \u003cp\u003e10.10 Frame-Free Form of the Lorentz Transformation 200\u003c\/p\u003e \u003cp\u003e10.11 Exercises 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Application of the Spacetime Geometric Algebra to Basic Electromagnetics 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Vector Potential and Some Spacetime Splits 204\u003c\/p\u003e \u003cp\u003e11.2 Maxwell’s Equations in Spacetime Form 208\u003c\/p\u003e \u003cp\u003e11.2.1 Maxwell’s Free Space or Microscopic Equation 208\u003c\/p\u003e \u003cp\u003e11.2.2 Maxwell’s Equations in Polarizable Media 210\u003c\/p\u003e \u003cp\u003e11.3 Charge Conservation and the Wave Equation 212\u003c\/p\u003e \u003cp\u003e11.4 Plane Electromagnetic Waves 213\u003c\/p\u003e \u003cp\u003e11.5 Transformation of the Electromagnetic Field 217\u003c\/p\u003e \u003cp\u003e11.5.1 A General Spacetime Split for \u003cb\u003e\u003ci\u003eF\u003c\/i\u003e\u003c\/b\u003e 217\u003c\/p\u003e \u003cp\u003e11.5.2 Maxwell’s Equation in a Different Frame 219\u003c\/p\u003e \u003cp\u003e11.5.3 Transformation of \u003cb\u003e\u003ci\u003eF\u003c\/i\u003e\u003c\/b\u003e by Replacement of Basis Elements 221\u003c\/p\u003e \u003cp\u003e11.5.4 The Electromagnetic Field of a Plane Wave Under a Change of Frame 223\u003c\/p\u003e \u003cp\u003e11.6 Lorentz Force 224\u003c\/p\u003e \u003cp\u003e11.7 The Spacetime Approach to Electrodynamics 227\u003c\/p\u003e \u003cp\u003e11.8 The Electromagnetic Field of a Moving Point Charge 232\u003c\/p\u003e \u003cp\u003e11.8.1 General Spacetime Form of a Charge’s Electromagnetic Potential 232\u003c\/p\u003e \u003cp\u003e11.8.2 Electromagnetic Potential of a Point Charge in Uniform Motion 234\u003c\/p\u003e \u003cp\u003e11.8.3 Electromagnetic Field of a Point Charge in Uniform Motion 237\u003c\/p\u003e \u003cp\u003e11.9 Exercises 240\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12. The Electromagnetic Field of a Point Charge Undergoing Acceleration 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Working with Null Vectors 243\u003c\/p\u003e \u003cp\u003e12.2 Finding \u003cb\u003e\u003ci\u003eF\u003c\/i\u003e\u003c\/b\u003e for a Moving Point Charge 248\u003c\/p\u003e \u003cp\u003e12.3 \u003cb\u003e\u003ci\u003eFrad\u003c\/i\u003e\u003c\/b\u003e in the Charge’s Rest Frame 252\u003c\/p\u003e \u003cp\u003e12.4 \u003cb\u003e\u003ci\u003eFrad\u003c\/i\u003e\u003c\/b\u003e in the Observer’s Rest Frame 254\u003c\/p\u003e \u003cp\u003e12.5 Exercises 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13. Conclusion 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14. Appendices 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Glossary 265\u003c\/p\u003e \u003cp\u003e14.2 Axial versus True Vectors 273\u003c\/p\u003e \u003cp\u003e14.3 Complex Numbers and the 2D Geometric Algebra 274\u003c\/p\u003e \u003cp\u003e14.4 The Structure of Vector Spaces and Geometric Algebras 275\u003c\/p\u003e \u003cp\u003e14.4.1 A Vector Space 275\u003c\/p\u003e \u003cp\u003e14.4.2 A Geometric Algebra 275\u003c\/p\u003e \u003cp\u003e14.5 Quaternions Compared 281\u003c\/p\u003e \u003cp\u003e14.6 Evaluation of an Integral in Equation (5.14) 283\u003c\/p\u003e \u003cp\u003e14.7 Formal Derivation of the Spacetime Vector Derivative 284\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eFurther Reading 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eThe IEEE Press Series on Electromagnetic Wave Theory\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402463191383,"sku":"9780470941638","price":109.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470941638.jpg?v=1730480481"},{"product_id":"principles-of-algebraic-geometry-9780471050599","title":"Principles of Algebraic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFoundational Material.\u003cbr\u003e \u003cbr\u003e Complex Algebraic Varieties.\u003cbr\u003e \u003cbr\u003e Riemann Surfaces and Algebraic Curves.\u003cbr\u003e \u003cbr\u003e Further Techniques.\u003cbr\u003e \u003cbr\u003e Surfaces.\u003cbr\u003e \u003cbr\u003e Residues.\u003cbr\u003e \u003cbr\u003e The Quadric Line Complex.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402482000215,"sku":"9780471050599","price":131.35,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471050599.jpg?v=1730480545"},{"product_id":"rigid-local-systems-9780691011189","title":"Rigid Local Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"It is clear that this book presents highly important new views and results on the classical theory of complex linear differential equations.\"--Zentralblatt fur Mathematik\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e* 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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403674722647,"sku":"9780691011189","price":74.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691011189.jpg?v=1730484221"},{"product_id":"nilpotence-and-periodicity-in-stable-homotopy-theory-9780691025728","title":"Nilpotence and Periodicity in Stable Homotopy","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDescribes 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"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 Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403686355287,"sku":"9780691025728","price":78.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691025728.jpg?v=1730484255"},{"product_id":"characteristic-classes-9780691081229","title":"Characteristic Classes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters\"\u003cbr\u003e\"John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society\"\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403712242007,"sku":"9780691081229","price":92.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691081229.jpg?v=1730484332"},{"product_id":"lectures-on-resolution-of-singularities-9780691129235","title":"Lectures on Resolution of Singularities","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eResolution 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"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, Mathematica\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction 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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403747533143,"sku":"9780691129235","price":51.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691129235.jpg?v=1730484430"},{"product_id":"some-problems-of-unlikely-intersections-in-arithmetic-and-geometry-9780691153704","title":"Some Problems of Unlikely Intersections in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eConsiders 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"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 Clippings\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403789377879,"sku":"9780691153704","price":180.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691153704.jpg?v=1730484547"},{"product_id":"mumfordtate-groups-and-domains-9780691154244","title":"MumfordTate Groups and Domains","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMumford-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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"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 Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction 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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403790295383,"sku":"9780691154244","price":170.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691154244.jpg?v=1730484551"},{"product_id":"a-course-on-surgery-theory-9780691160498","title":"A Course on Surgery Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403803533655,"sku":"9780691160498","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691160498.jpg?v=1730484592"},{"product_id":"nonarchimedean-tame-topology-and-stably-dominated-types-9780691161686","title":"NonArchimedean Tame Topology and Stably Dominated","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eOver 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-archimed\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry.\"\u003cb\u003e---Anand Pillay, \u003ci\u003eMathSciNet\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403805827415,"sku":"9780691161686","price":130.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691161686.jpg?v=1730484601"},{"product_id":"nonarchimedean-tame-topology-and-stably-dominated-types-9780691161693","title":"NonArchimedean Tame Topology and Stably Dominated","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry.\"\u003cb\u003e---Anand Pillay, \u003ci\u003eMathSciNet\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403805860183,"sku":"9780691161693","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691161693.jpg?v=1730484600"},{"product_id":"descent-in-buildings-9780691166919","title":"Descent in Buildings","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eDescent 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 f\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"An impressive tour de force.\"--Bertrand Remy, Jahresbericht der DMV\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi  PART 1. MOUFANG QUADRANGLES 1\t  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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403817820503,"sku":"9780691166919","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691166919.jpg?v=1730484635"},{"product_id":"fourier-restriction-for-hypersurfaces-in-three-dimensions-and-newton-polyhedra-9780691170541","title":"Fourier Restriction for Hypersurfaces in Three","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*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) =\u0026gt; 2: Preparatory Results, pg. 105*Chapter 7. How to Go beyond the Case hlin(PHI) =\u0026gt; 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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403827454295,"sku":"9780691170541","price":130.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691170541.jpg?v=1730484659"},{"product_id":"etale-cohomology-9780691171104","title":"Étale Cohomology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Terminology and Conventions, pg. xiii*Chapter I. Etale Morphisms, pg. 1*Chapter II. Sheaf Theory, pg. 46*Chapter III. Cohomology, pg. 82*Chapter IV. The Brauer Group, pg. 136*Chapter V. The Cohomology of Curves and Surfaces, pg. 155*Chapter VI. The Fundamental Theorems, pg. 220*Appendix A. Limits, pg. 304*Appendix B. Spectral Sequences, pg. 307*Appendix C. Hypercohomology, pg. 310*Bibliography, pg. 313*Index, pg. 321","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403828732247,"sku":"9780691171104","price":38.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691171104.jpg?v=1730484663"},{"product_id":"the-norm-residue-theorem-in-motivic-cohomology-9780691191041","title":"The Norm Residue Theorem in Motivic Cohomology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403872674135,"sku":"9780691191041","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691191041.jpg?v=1730484761"},{"product_id":"what-determines-an-algebraic-variety-9780691246819","title":"What Determines an Algebraic Variety","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403928510807,"sku":"9780691246819","price":52.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691246819.jpg?v=1730484913"},{"product_id":"groups-rings-and-group-rings-9781584885818","title":"Groups, Rings and Group Rings","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. 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.","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49410387214679,"sku":"9781584885818","price":228.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781584885818.jpg?v=1730510046"},{"product_id":"ideals-of-powers-and-powers-of-ideals-intersecting-algebra-geometry-and-combinatorics-9783030452469","title":"Ideals of Powers and Powers of Ideals:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning  our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms.  Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes\u003ci\u003e.\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This is a very interesting monograph providing a fast introduction to different fields of research devoted to modern aspects and develompents of commutative algebra, algebraic geometry, combinatorics, etc.” (Piotr Pokora, zbMATH 1445.13001, 2020)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- \u003cb\u003ePart I Associated Primes of Powers of Ideals\u003c\/b\u003e - Associated Primes of Powers of Ideals. - Associated Primes of Powers of Squarefree Monomial Ideals. - Final Comments and Further Reading. - \u003cb\u003ePart II Regularity of Powers of Ideals. \u003c\/b\u003e- Regularity of Powers of Ideals and the Combinatorial Framework. - Problems, Questions, and Inductive Techniques. - Examples of the Inductive Techniques. - Final Comments and Further Reading. - \u003cb\u003ePart III The Containment Problem.\u003c\/b\u003e - The Containment Problem: Background. - The Containment Problem. - The Waldschmidt Constant of Squarefree Monomial Ideals. - Symbolic Defect. - Final Comments and Further Reading. - \u003cb\u003ePart IV Unexpected Hypersurfaces.\u003c\/b\u003e - Unexpected Hypersurfaces. - Final Comments and Further Reading.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415620919639,"sku":"9783030452469","price":50.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030452469.jpg?v=1730527545"},{"product_id":"arithmetic-geometry-number-theory-and-computation-9783030809133","title":"Arithmetic Geometry, Number Theory, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research.\u003cbr\u003eSpecific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e  A robust implementation for solving the S-unit equation and several application (C. Rasmussen).- Computing classical modular forms for arbitrary congruence subgroups (E. Assaf).- Square root time Coleman integration on superelliptic curves (A. Best).- Computing classical modular forms ( A. Sutherland).- Elliptic curves with good reduction outside of the first six primes (B. Matschke).- Efficient computation of BSD invariants in genus 2 (R. van Bommel).- Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (E. Costa).- Zen and the art of database maintenance (D. Roe).- Effective obstructions to lifting Tate classes from positive characteristic (E. Costa).- Conjecture: 100% of elliptic surfaces over Q have rank zero (A. Cowan).- On rational Bianchi newforms and abelian surfaces with quaternionic multiplication (J. Voight).- A database of Hilbert modular forms (J. Voight).- Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB (D. Roe).- Computing rational points on genus 3 hyperelliptic curves (S. Hashimoto).- Curves with sharp Chabauty-Coleman bound (S. Gajović).- Chabauty-Coleman computations on rank 1 Picard curves (S. Hashimoto).- Linear dependence among Hecke eigenvalues (D. Kim).- Congruent number triangles with the same hypotenuse (D. Lowry-Duda).- Visualizing modular forms (D. Lowry-Duda).- A Prym variety with everywhere good reduction over \u003cb\u003eQ\u003c\/b\u003e(√ 61) ( J. Voight).- The S-integral points on the projective line minus three points via étale covers and Skolem's method (B. Poonen).\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415643038039,"sku":"9783030809133","price":159.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030809133.jpg?v=1730527626"},{"product_id":"topics-in-global-real-analytic-geometry-9783030966652","title":"Topics in Global Real Analytic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIn the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert’s problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert’s problem implies a solution for the real Nullstellensatz more similar to the one for real polinomials. A chapter is devoted to the state of the art on this problem that is far from a complete answer.\u003c\/p\u003e \u003cp\u003eIn the last chapter we deal with inequalities. We describe a class of semianalytic sets defined by countably many global real analytic functions that is stable under topological properties and under proper holomorphic maps between Stein spaces, that is, verifies a direct image theorem. A smaller class admits also a decomposition into irreducible components as it happens for semialgebraic sets. During the redaction some proofs have been simplified with respect to the original ones.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book presents nice results in the overlapping of real analytic geometry, complex analytic geometry and real algebraic geometry. It is well written. The introduction describes the historical developments in a very motivating way. The existing literature is well addressed. The book is intended for researchers or PhD students with a background in complex analysis (in several variables) and commutative algebra. It is dedicated to the memory of Alberto Tognoli.” (Tobias Kaiser, Mathematical Reviews, June, 2023)\u003cbr\u003e\u003cbr\u003e“This noteworthy book fulfills the goal of giving an excellently well written account of the present state of a number of relevant topics in the field of Real Analytic Geometry.” (José Javier Etayo, zbMATH 1495.14001, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction\u003c\/p\u003e \u003cp\u003eChapter 1. The class of C-analytic spaces \u003c\/p\u003e \u003cp\u003eChapter 2. More on analytic sets\u003c\/p\u003e \u003cp\u003eChapter 3. Nullstellensätze\u003c\/p\u003e \u003cp\u003eChapter 4. The 17th Hilbert’s Problem for real analytic functions\u003c\/p\u003e \u003cp\u003eChapter 5. Analytic inequalities\u003c\/p\u003e \u003cp\u003eReferences\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415668138327,"sku":"9783030966652","price":94.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030966652.jpg?v=1730527718"},{"product_id":"the-art-of-doing-algebraic-geometry-9783031119378","title":"The Art of Doing Algebraic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eM. C. Brambilla, O. Dumitrescu, E. Postinghel, “Weyl cycles on the blow-up of $P^4$ at eight points\".- A. Brigaglia, “Simson’s reconstruction of Apollonius’ Loci Plani. Modern ideas in classical language”.- F. Catanese, “Kummer quartic surfaces, strict self-duality, and more”.- L. Chiantini e Giorgio Ottaviani, “A footnote to a footnote to a paper of B. Segre”.- T. Dedieu and E. Sernesi, “Deformations and extensions of Gorenstein weighted projective spaces”.- V. Di Gennaro and Davide Franco, “Intersection cohomology and Severi Varieties”.- O. Dumitrescu and R. Miranda, “Cremona Orbits in $\\mathbb P^4$ and Applications”.- F. Flamini and P. Supino, “On some components of Hilbert schemes of curves”.- Gerard van der Geer, “Siegel modular forms of degree two and three and invariant theory”.- A. Laface and L. Ugaglia, “On intrinsic negative curves”.- Angelo F. Lopez, with an appendix by Thomas Dedieu, “On the extendibility of projective varieties: a survey”.- M. Mella, “The minimal Cremona degree of quartic surfaces”.- M. Mendes Lopes and R. Pardini, “On the degree of the canonical map of a surface of general type”.- C. Pedrini, “Hyperkæhler varieties with a motive of abelian type”.- F. Polizzi and P. Sabatino, “Finite quotients of surface braid groups and double Kodaira fibrations”.- Y. Prokhorov and M. Zaidenberg, “Affine cones over Fano-Mukai fourfolds of genus 10 are flexible”.- J. Roé, “Enriques diagrams under pullback by a double cover”.- E. Rogora, “The “projective spirit” in Segre’s lectures on differential equations”.\u003cbr\u003e \u003cp\u003e \u003c\/p\u003e","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49415685079383,"sku":"9783031119378","price":87.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031119378.jpg?v=1730527784"},{"product_id":"dialogues-between-physics-and-mathematics-c-n-yang-at-100-9783031175220","title":"Dialogues Between Physics and Mathematics: C. N.","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the \u003ci\u003eDialogue Between Physics and Mathematics\u003c\/i\u003e that has been a central theme of Professor Yang’s contributions to contemporary science. Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry.\u003cbr\u003eInspired by the original ideas of C. N. Yang, this unique collection of papers b masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Frank Yang at Stony Brook and the Beginning of Supergravity.- 2. A Stacky Approach to Crystals.- 3 The Potts Model, the Jones Polynomial and Link Homology.- 4 The Penrose–Onsager–Yang Approach to Superconductivity and Superfluidity.- 5 Quantum Operads.- 6 Quantum computational complexity with\u003cbr\u003ephotons and linear optics.- 7 Quantized Twistors, G2*, and the Split Octonions.- 8 Kronecker Anomalies and Gravitational Striction.- 9 Projecting Local and Global Symmetries to the Planck Scale.- 10 Gauge Symmetry in Shape Dynamics.- 11 Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?.- 12 Quantum Anomalous Hall Effect.- 13 Magic Superconducting States in Cuprates.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415692812631,"sku":"9783031175220","price":87.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031175220.jpg?v=1730527808"},{"product_id":"birational-geometry-kahler-einstein-metrics-and-degenerations-moscow-shanghai-and-pohang-april-november-2019-9783031178580","title":"Birational Geometry, Kähler–Einstein Metrics and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang\u003c\/p\u003e\u003cp\u003eThe conferences were focused on the following two related problems:\u003c\/p\u003e\u003cp\u003e•  existence of Kähler–Einstein metrics on Fano varieties\u003c\/p\u003e\u003cp\u003e•  degenerations of Fano varieties\u003c\/p\u003e\u003cp\u003eon which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide.\u003c\/p\u003e\u003cp\u003eThese conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eT. Abe, Classification of exceptional complements: elliptic curve case.- E. Ballico, E. Gasparim, F. Rubilar, B. Suzuki, LAGRANGIAN SKELETA, COLLARS AND DUALITY.- G. Belousov, CYLINDERS IN DEL PEZZO SURFACES OF DEGREE TWO.- M. Benzerga, FINITENESS OF REAL STRUCTURES ON KLT CALABI-YAU REGULAR SMOOTH PAIRS OF DIMENSION 2.- C. Birkar, ANTICANONICAL VOLUME OF FANO 4-FOLDS.- C. Boyer Christina Tonnesen-Friedman, CONSTANT SCALAR CURVATURE SASAKI METRICS AND PROJECTIVE BUNDLES.- G. Brown, J. Buczynski, A. Kasprzyk, TORIC SARKISOV LINKS.- I. Burban, DU VAL SINGULARITIES.- I. Cheltsov, H. Suess, K-POLYSTABILITY OF TWO SMOOTH FANO THREEFOLDS.- G. Codogni, Z. Patakfalvi, A NOTE ON FAMILIES OF K-SEMISTABLE LOG-FANO PAIRS.- T. Delcroix, THE YAU-TIAN-DONALDSON CONJECTURE FOR COHOMOGENEITY ONE MANIFOLDS.- A. Dubouloz, FIBRATIONS BY AFFINE LINES ON RATIONAL AFFINE SURFACES WITH IRREDUCIBLE BOUNDARIES.- K. Fujita, ON FANO THREEFOLDS OF DEGREE 22 AFTER CHELTSOV AND SHRAMOV.- K. Fujita, Y. Liu, H. Suess, K. Zhang, Z. Zhuang, ON THE CHELTSOV-RUBINSTEIN CONJECTURE.- S. Grishin, Ilya Karzhemanov, Ming-Chang Kang, RATIONALITY OF QUOTIENTS BY FINITE HEISENBERG GROUPS.- Y. Hashimoto.- J. Keller, QUOT-SCHEME LIMIT OF FUBINI–STUDY METRICS AND ITS APPLICATIONS TO BALANCED METRICS.- Z. Hu, EXISTENCE OF CANONICAL MODELS FOR KAWAMATA LOG TERMINAL PAIRS.- Y. Imagi, GENERALIZED THOMAS–YAU UNIQUENESS THEOREMS.- K. Jamieson, BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION 3.- D. Jeong.- J. Park, SIMPLY CONNECTED SASAKI-EINSTEIN 5-MANIFOLDS: OLD AND NEW.- C. Jiang, CHARACTERIZING Q-FANO THREEFOLDS WITH THE SMALLEST ANTI-CANONICAL VOLUME.- L. Katzarkov, Kyoung-Seog Lee, J. Svoboda, A. Petkov, INTERPRETATIONS OF SPECTRA.- Young-Hoon Kiem, Kyoung-Seog Lee, FANO VISITORS, FANO DIMENSION AND FANO ORBIFOLDS.- In-kyun Kim, N. Viswanathan, J. Won, ON SINGULAR DEL PEZZO HYPERSURFACES OF INDEX 3.- S. Kudryavtsev, Blow-ups of three-dimensional toric singularities.- N. Kurnosov, E. Yasinsky, AUTOMORPHISMS OF HYPERKAHLER MANIFOLDS AND GROUPS ACTING ON CAT(0) SPACES.- A. Laface, R. Quezada, ON GENERALIZED BUCHI SURFACES.- Chi Li, K-STABILITY AND FUJITA APPROXIMATION.- Y. Li, Zhenye Li, ON A CONJECTURE OF FULTON ON ISOTROPIC GRASSMANNIANS.- Y. Maeda, Y. Odaka, FANO SHIMURA VARIETIES WITH MOSTLY BRANCHED CUSP.- L. Makar-Limanov, ON LOCALLY NILPOTENT DERIVATIONS OF DANIELEWSKI DOMAINS.- D. Markouchevitch, A. Moreau, ACTION OF THE AUTOMORPHISM GROUP ON THE JACOBIAN OF KLEIN'S QUARTIC CURVE.- J. Martinez-Garcia, C. Spotti, SOME OBSERVATIONS ON THE DIMENSION OF FANO K-MODULI.- D. Witt Nystrom, OKOUNKOV BODIES AND THE KAHLER GEOMETRY OF PROJECTIVE MANIFOLDS.- J. Park, SINGULARITIES OF PLURI-FUNDAMENTAL DIVISORS ON GORENSTEIN FANO VARIETIES OF COINDEX.-  J. Paulhus, A DATABASE OF GROUP ACTIONS ON RIEMANN SURFACES.- A. Petracci, A 1-DIMENSIONAL COMPONENT OF K-MODULI OF DEL PEZZO SURFACES.- T. De Piro, A NON-STANDARD BEZOUT THEOREM FOR CURVES.- Y. Prokhorov, EMBEDDINGS OF THE SYMMETRIC GROUPS TO THE SPACE CREMONA GROUP.- J. Ross, M. Toma, ON HODGE-RIEMANN COHOMOLOGY CLASSES.- Y. Rubinstein, ON LARGE DEVIATION PRINCIPLES AND THE MONGE–AMPERE EQUATION (FOLLOWING BERMAN, HULTGREN).- T. Sano, ON BIRATIONAL BOUNDEDNESS OF SOME CALABI-YAU HYPERSURFACES.- Y. Zarhin, ABELIAN VARIETIES, QUATERNION TRICK AND ENDOMORPHISMS.\u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415693369687,"sku":"9783031178580","price":135.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031178580.jpg?v=1730527811"},{"product_id":"empowering-novel-geometric-algebra-for-graphics-and-engineering-7th-international-workshop-engage-2022-virtual-event-september-12-2022-proceedings-9783031309229","title":"Empowering Novel Geometric Algebra for Graphics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book constitutes the proceedings of the Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2022, held in conjunction with Computer Graphics International conference, CGI 2022, which took place virtually, in September 2022. \u003c\/p\u003e  The 10 full papers included in this volume were carefully reviewed and selected from 12 submissions. The workshop focused specifically on important aspects of geometric algebra including algebraic foundations, digitized transformations, orientation, conic fitting, protein modelling, digital twinning, and multidimensional signal processing.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFoundations of Geometric Algebra.- Transformations, Orientation and Fitting.- Modelling Proteins and Cities.- Signal Processing with Octonions.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415707165015,"sku":"9783031309229","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031309229.jpg?v=1730527856"},{"product_id":"the-padic-simpson-correspondence-and-hodgetate-local-systems-9783031559136","title":"The PAdic Simpson Correspondence and HodgeTate","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":49415737311575,"sku":"9783031559136","price":43.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031559136.jpg?v=1730527940"},{"product_id":"arithmetic-geometry-over-global-function-fields-9783034808521","title":"Arithmetic Geometry over Global Function Fields","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCohomological Theory of Crystals over Function Fields and Applications.- On Geometric Iwasawa Theory and Special Values of Zeta Functions.- The Ongoing Binomial Revolution.- Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields.- Curves and Jacobians over Function Fields.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49415774175575,"sku":"9783034808521","price":31.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783034808521.jpg?v=1730528050"},{"product_id":"complex-geometry-an-introduction-9783540212904","title":"Complex Geometry: An Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eEasily accessible \u003c\/p\u003e \u003cp\u003eIncludes recent developments\u003c\/p\u003e \u003cp\u003eAssumes very little knowledge of differentiable manifolds and functional analysis\u003c\/p\u003e \u003cp\u003eParticular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"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. [...]\u003c\/p\u003e \u003cp\u003eThe author has added two general appendices at the end of the book. Those are\u003cbr\u003emeant 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.\"\u003c\/p\u003e \u003cp\u003e\u003cem\u003eKIeinert (Berlin), Zentralblatt für Mathematik 1055 (2005)\u003c\/em\u003e \u003c\/p\u003e \u003cp\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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. \u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eThus 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.\u003c\/p\u003e \u003cp\u003e\u003cem\u003eProfessor Dominique LAMBERT, University of Namur; Department « sciences, philosophies et sociétés » Rue de Bruxelles 61 B-5000 Namur Belgium\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"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)\u003c\/p\u003e \u003cp\u003e\"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)\u003c\/p\u003e \u003cp\u003e\"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)\u003c\/p\u003e \u003cp\u003e\"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)\u003c\/p\u003e \u003cp\u003e\"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)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eLocal Theory.- Complex Manifolds.- Kähler Manifolds.- Vector Bundles.- Applications of Cohomology.- Deformations of Complex Structures.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49419499405655,"sku":"9783540212904","price":61.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540212904.jpg?v=1730538541"},{"product_id":"algebraic-theory-of-locally-nilpotent-derivations-9783662553480","title":"Algebraic Theory of Locally Nilpotent Derivations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. \u003c\/p\u003e\u003cp\u003eThe author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eMore recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14\u003csup\u003eth\u003c\/sup\u003e Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eA lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- 1 First Principles.- 2 Further Properties of LNDs.- 3 Polynomial Rings.- 4 Dimension Two.- 5 Dimension Three.- 6 Linear Actions of Unipotent Groups.- 7 Non-Finitely Generated Kernels.- 8 Algorithms.- 9 Makar-Limanov and Derksen Invariants.- 10 Slices, Embeddings and Cancellation.- 11 Epilogue.- References.- Index.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49420190548311,"sku":"9783662553480","price":95.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783662553480.jpg?v=1730541103"},{"product_id":"collected-works-9783662621332","title":"Collected Works","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWhile Eugenio Calabi is best known for his contributions to the theory of Calabi-Yau manifolds, this Steele-Prize-winning geometer’s fundamental contributions to mathematics have been far broader and more diverse than might be guessed from this one aspect of his work. His works have deep influence and lasting impact in global differential geometry, mathematical physics and beyond. By bringing together 47 of Calabi’s important articles in a single volume, this book provides a comprehensive overview of his mathematical oeuvre, and includes papers on complex manifolds, algebraic geometry, Kähler metrics, affine geometry, partial differential equations, several complex variables, group actions and topology. The volume also includes essays on Calabi’s mathematics by several of his mathematical admirers, including S.K. Donaldson, B. Lawson and S.-T. Yau, Marcel Berger; and Jean Pierre Bourguignon. This book is intended  for mathematicians and graduate students around the world. Calabi’s visionary contributions will certainly continue to shape the course of this subject far into the future.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“In my case, I spent several happy hours learning about affine differential geometry, something that would certainly never have happened if I had not picked up this volume. … The collected works of Eugenio Calabi are worthy of a place on the bookshelf of any person with a serious interest in differential geometry.” (Joel Fine, EMS Magazine, May 11, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.-  J.-P. Bourguignon, Eugenio Calabi’s Short Biography.- Bibliographic List of Works.- S.-T. Yau, An Essay on Eugenio Calabi.- Part I: Commentaries on Calabi’s Life and Work: B. Lawson, Reflections on the Early Work of Eugenio Calabi.- M. Berger, Encounter with a Geometer: Eugenio Calabi.- J.-P. Bourguignon, Eugenio Calabi and Kähler Metrics.- C. LeBrun, Eugenio Calabi and the Curvature of Kähler Manifolds.- X. Chen, S. Donaldson, Calabi’s Work on Affine Differential Geometry and Results of Bernstein Type.- Part II: Collected Works: E. Calabi ,Ar. Dvoretzky, Convergence- and Sum-Factors for Series of Complex Numbers (1951).- E. Calabi, D. C. Spencer, Completely Integrable Almost Complex Manifolds (1951).- E. Calabi, Metric Riemann Surfaces (1953).- E. Calabi, M. Rosenlicht, Complex Analytic Manifolds Without Countable Base (1953).- E. Calabi, B. Eckmann, A Class of Compact, Complex Manifolds Which Are Not Algebraic (1953).- E. Calabi, Isometric Imbedding of Complex Manifolds (1953).- E. Calabi, The Space of Kähler Metrics (1954).- E. Calabi, The Variation of Kähler Metrics I. The Structure of the Space (1954).- E. Calabi, The Variation of Kähler Metrics II. A Minimum Problem (1954).- E. Calabi, On Kähler Manifolds With Vanishing Canonical Class (1957).- E. Calabi, Construction and Properties of Some 6-Dimensional Almost Complex Manifolds (1958).- E. Calabi, Improper Affine Hyperspheres of Convex Type and a Generalization of a Theorem by K. Jörgens (1958).- E. Calabi, An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1958).- E. Calabi, Errata: An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1959).- E. Calabi, E. Vesentini, Sur les variétés complexes compactes localement symétriques (1959).- E. Calabi, E. Vesentini, On Compact, Locally Symmetric Kähler Manifolds (1960).- E. Calabi, On Compact, Riemannian Manifolds with Constant Curvature I. (1961).- E. Calabi, L. Markus Relativistic Space Forms (1962).- E. Calabi, Linear Systems of Real Quadratic Forms (1964).- E. Calabi, Quasi-Surjective Mappings and a Generalization of Morse Theory (1966).- E. Calabi, Minimal Immersions of Surfaces in Euclidean Spheres (1967).- E. Calabi, On Ricci Curvature and Geodesics (1967).- E. Calabi, On Differentiable Actions of Compact Lie Groups on Compact Manifolds (1968).- E. Calabi, An Intrinsic Characterization of Harmonic One-Forms (1969).- E. Calabi, On the Group of Automorphisms of a Symplectic Manifold (1970).- E. Calabi, P. Hartman, On the Smoothness of Isometries (1970).- E. Calabi, Examples of Bernstein Problems for Some Nonlinear Equations (1970).- E. Calabi, Über singuläre symplektische Strukturen (1971).- E. Calabi, Complete Affine Hyperspheres I (1972).- E. Calabi, A Construction of Nonhomogeneous Einstein Metrics (1975).- E. Calabi, H. S. Wilf, On the Sequential and Random Selection of Subspaces Over a  Finite Field (1977).- E. Calabi, Métriques kählériennes et fibrés  holomorphes (1978).- E. Calabi, Isometric Families of Kähler Structures (1980).- E. Calabi, Géométrie différentielle affine des  hypersurfaces (1981).- E. Calabi, Linear Systems of Real Quadratic Forms II (1982).- E. Calabi, Extremal Kähler Metrics (1982).- E. Calabi, Hypersurfaces with Maximal Affinely Invariant Area (1982).- E. Calabi, Extremal Kähler Metrics II (1985).- E. Calabi, Convex Affine Maximal Surfaces (1988).- E. Calabi, Affine Differential Geometry and Holomorphic Curves (1990).- E. Calabi, J. Cao Simple Closed Geodesics on Convex Surfaces (1992).- F. Beukers, J. A. C. Kolk and E. Calabi, Sums of Generalized Harmonic Series and Volumes (1993).- E. Calabi and H. Gluck, What are the Best Almost-Complex Structures on the 6-Sphere? (1993).- E. Calabi, Extremal Isosystolic Metrics for Compact Surfaces (1996).- E. Calabi, P. J. Olver, A. Tannenbaum, Affine Geometry, Curve Flows, and Invariant Numerical Approximations (1996).- J.-P. Bourguignon, E. Calabi, J. Eells, O. Garcia-Prada, M. Gromov,  Where Does Geometry Go? A Research and Education Perspective (2001).- E. Calabi, X. Chen, The Space of Kähler Metrics II (2002).- Acknowledgements. \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49420202869079,"sku":"9783662621332","price":123.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783662621332.jpg?v=1730541146"},{"product_id":"rigid-germs-the-valuative-tree-and-applications-to-kato-varieties-9788876425585","title":"Rigid Germs, the Valuative Tree, and Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds.\u003c\/p\u003e\u003cp\u003eThe local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates.\u003c\/p\u003e\u003cp\u003eIn dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple.\u003c\/p\u003e\u003cp\u003e      \u003c\/p\u003e\u003cp\u003eIn some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction.-1.Background.- 2.Dynamics in 2D.- 3.Rigid germs in higher dimension.- 4 Construction of non-Kahler 3-folds.- References.- Index.\u003c\/p\u003e","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49427425755479,"sku":"9788876425585","price":13.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788876425585.jpg?v=1730564501"},{"product_id":"nevanlinna-theory-9789811067860","title":"Nevanlinna Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from \u003cb\u003eC\u003c\/b\u003e to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface1. Nevanlinna Theory of One Variable (1)1.1 metrics of compact Rimann surfaces1.2 integral formula1.3 holomorphic maps over compact Riemann surfaces whose genus are greater than 21.4 holomorphic maps over Riemann sphreres1.5 Defect relation\u003cbr\u003e2. Schwarz--Kobayashi's Lemma2.1 Schwarz--Kobayashi's Lemma2.2 holomorphic maps over algebraic varieties (general type)2.3 hyperbolic measures\u003cbr\u003e3. Nevanlinna Theory of One Variable (2)3.1 holomorphic maps over Riemann shpres3.2 the first main theorem3.3 the second main theorem\u003cbr\u003e4.  Nevanlinna Theory of Several Variables4.1 Biebelbach's example4.2 the first main theorem4.3 the second main theorem4.4 defect relation4.5 applications\u003cbr\u003eReferences","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427818283351,"sku":"9789811067860","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811067860.jpg?v=1730565781"},{"product_id":"algebraic-geometry-9780387902449","title":"Algebraic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eI Varieties.- II Schemes.- III Cohomology.- IV Curves.- V Surfaces.- Appendix A Intersection Theory.- 1 Intersection Theory.- 2 Properties of the Chow Ring.- 3 Chern Classes.- 4 The Riemann-Roch Theorem.- 5 Complements and Generalizations.- Appendix B Transcendental Methods.- 1 The Associated Complex Analytic Space.- 2 Comparison of the Algebraic and Analytic Categories.- 3 When is a Compact Complex Manifold Algebraic?.- 4 Kähler Manifolds.- 5 The Exponential Sequence.- Appendix C The Weil Conjectures.- 1 The Zeta Function and the Weil Conjectures.- 2 History of Work on the Weil Conjectures.- 3 The \/-adic Cohomology.- 4 Cohomological Interpretation of the Weil Conjectures.- Results from Algebra.- Glossary of Notations.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eR. Hartshorne\u003c\/p\u003e \u003cp\u003e\u003cem\u003eAlgebraic Geometry\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions.\"—\u003c\/em\u003eMATHEMATICAL REVIEWS\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction. 1: Varieties. 2: Schemes. 3: Cohomology. 4: Curves. 5: Surfaces. Appendix A: Intersection Theory. B: Transcendental Methods. C: The Weil Conjectures. Bibliography. Results from Algebra. Glossary of Notations. Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49525117649239,"sku":"9780387902449","price":33.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387902449.jpg?v=1731859289"},{"product_id":"linear-algebra-for-the-young-mathematician-9781470450847","title":"Linear Algebra for the Young Mathematician","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides a careful, thorough, and rigorous introduction to linear algebra. The book adopts a conceptual point of view, focusing on the notions of vector spaces and linear transformations, and it takes pains to provide proofs that bring out the essential ideas of the subject.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eVector spaces: The basics\u003c\/li\u003e\n\u003cli\u003eSystems of linear equations\u003c\/li\u003e\n\u003cli\u003eVector spaces\u003c\/li\u003e\n\u003cli\u003eLinear transformations\u003c\/li\u003e\n\u003cli\u003eMore on vector spaces and linear transformations\u003c\/li\u003e\n\u003cli\u003eThe determinant\u003c\/li\u003e\n\u003cli\u003eThe structure of a linear transformation\u003c\/li\u003e\n\u003cli\u003eJordan canonical form\u003c\/li\u003e\n\u003cli\u003eVector spaces with additional structure: Forms on vector spaces\u003c\/li\u003e\n\u003cli\u003eInner product spaces\u003c\/li\u003e\n\u003cli\u003eFields\u003c\/li\u003e\n\u003cli\u003ePolynomials\u003c\/li\u003e\n\u003cli\u003eNormed vector spaces and questions of analysis\u003c\/li\u003e\n\u003cli\u003eA guide to further reading\u003c\/li\u003e\n\u003cli\u003eIndex.\u003c\/li\u003e\n\u003cli\u003e\u003cul\u003e\u003c\/ul\u003e\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":49530532528471,"sku":"9781470450847","price":74.1,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470450847.jpg?v=1731879624"}],"url":"https:\/\/bookcurl.com\/collections\/algebraic-geometry.oembed?page=2","provider":"Book Curl","version":"1.0","type":"link"}