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New Trends In Algebraic Geometry And Its Applications
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Book Synopsis New Trends in Algebraic Geometry by : Klaus Hulek
Download or read book New Trends in Algebraic Geometry written by Klaus Hulek and published by Cambridge University Press. This book was released on 1999-05-13 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing 17 survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A,D,E classification, centred around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric foundations to mirror symmetry; and two deep, informative surveys by Siebert and Behrend on Gromow-Witten invariants treating them from the point of view of algebraic and symplectic geometry. The remaining articles cover a wide cross-section of the most significant research topics in algebraic geometry. This includes Gromow-Witten invariants, Hodge theory, Calabi-Yau 3-folds, mirror symmetry and classification of varieties.
Book Synopsis Algebraic Geometry and Its Applications by : Jean Chaumine
Download or read book Algebraic Geometry and Its Applications written by Jean Chaumine and published by World Scientific. This book was released on 2008 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
Book Synopsis Recent Trends in Algebraic Combinatorics by : Hélène Barcelo
Download or read book Recent Trends in Algebraic Combinatorics written by Hélène Barcelo and published by Springer. This book was released on 2019-01-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.
Book Synopsis A Study in Derived Algebraic Geometry by : Dennis Gaitsgory
Download or read book A Study in Derived Algebraic Geometry written by Dennis Gaitsgory and published by American Mathematical Society. This book was released on 2019-12-31 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a “renormalization” of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $mathrm{(}infty, 2mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $mathrm{(}infty, 2mathrm{)}$-categories needed for the third part.
Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Book Synopsis Noncommutative Algebraic Geometry by : Gwyn Bellamy
Download or read book Noncommutative Algebraic Geometry written by Gwyn Bellamy and published by Cambridge University Press. This book was released on 2016-06-20 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.
Book Synopsis Commutative Algebra and its Applications by : Marco Fontana
Download or read book Commutative Algebra and its Applications written by Marco Fontana and published by Walter de Gruyter. This book was released on 2009-09-04 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected refereed papers based on lectures presented at the ‘Fifth International Fez Conference on Commutative Algebra and Applications’ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
Book Synopsis Algebraic Geometry and Geometric Modeling by : Mohamed Elkadi
Download or read book Algebraic Geometry and Geometric Modeling written by Mohamed Elkadi and published by Springer Science & Business Media. This book was released on 2006-11-02 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects.
Book Synopsis Algebraic Geometry by : Robin Hartshorne
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Book Synopsis Fundamental Algebraic Geometry by : Barbara Fantechi
Download or read book Fundamental Algebraic Geometry written by Barbara Fantechi and published by American Mathematical Soc.. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
Book Synopsis Current Developments in Algebraic Geometry by : Lucia Caporaso
Download or read book Current Developments in Algebraic Geometry written by Lucia Caporaso and published by Cambridge University Press. This book was released on 2012-03-19 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.
Book Synopsis Mordell–Weil Lattices by : Matthias Schütt
Download or read book Mordell–Weil Lattices written by Matthias Schütt and published by Springer Nature. This book was released on 2019-10-17 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.
Book Synopsis Number Theory and Algebraic Geometry by : Miles Reid
Download or read book Number Theory and Algebraic Geometry written by Miles Reid and published by Cambridge University Press. This book was released on 2003 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.
Book Synopsis New Trends in Geometry by : Luciano Boi
Download or read book New Trends in Geometry written by Luciano Boi and published by World Scientific. This book was released on 2011 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines. The integration of mathematics with physics, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines.
Book Synopsis Groups St Andrews 2001 in Oxford: Volume 1 by : C. M. Campbell
Download or read book Groups St Andrews 2001 in Oxford: Volume 1 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2003-11-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions from Marston Conder (Auckland), Persi Diaconis (Stanford) and Marcus Du Sautoy (Cambridge). The series of Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past twenty years. As with earlier volumes, these refereed volumes also contain accessible surveys of contemporary research fronts, as well as a diverse collection of short research articles. They form a valuable reference for researchers, especially graduate students, working in group theory.
Book Synopsis Algebraic Methods in Statistics and Probability by : Marlos A. G. Viana
Download or read book Algebraic Methods in Statistics and Probability written by Marlos A. G. Viana and published by American Mathematical Soc.. This book was released on 2001 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 23 papers report recent developments in using the technique to help clarify the relationship between phenomena and data in a number of natural and social sciences. Among the topics are a coordinate-free approach to multivariate exponential families, some rank-based hypothesis tests for covariance structure and conditional independence, deconvolution density estimation on compact Lie groups, random walks on regular languages and algebraic systems of generating functions, and the extendibility of statistical models. There is no index. c. Book News Inc.
Book Synopsis New Trends in Hopf Algebra Theory by : Nicolás Andruskiewitsch
Download or read book New Trends in Hopf Algebra Theory written by Nicolás Andruskiewitsch and published by American Mathematical Soc.. This book was released on 2000 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the Colloquium on Quantum Groups and Hopf Algebras held in Cordoba (Argentina) in 1999. The meeting brought together researchers who discussed recent developments in Hopf algebras, one of the most important being the influence of quantum groups. Articles offer introductory expositions and surveys on topics of current interest that, to date, have not been available in the current literature. Surveys are included on characteristics of Hopf algebras and their generalizations, biFrobenius algebras, braided Hopf algebras, inner actions and Galois theory, face algebras, and infinitesimal Hopf algebras. The following topics are also covered: existence of integrals, classification of semisimple and pointed Hopf algebras, *-Hopf algebras, dendriform algebras, etc. Non-classical topics are also included, reflecting its applications both inside and outside the theory.
