Geometric Methods in Algebra and Number Theory

Geometric Methods in Algebra and Number Theory
Author: Fedor Bogomolov
Publisher: Springer Science & Business Media
Total Pages: 384
Release: 2004-11-12
Genre: Mathematics
ISBN: 9780817643492
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* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

Geometric Methods in Algebra and Number Theory

Geometric Methods in Algebra and Number Theory
Author: Fedor Bogomolov
Publisher: Springer Science & Business Media
Total Pages: 365
Release: 2006-06-22
Genre: Mathematics
ISBN: 0817644172
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* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

Geometric Methods in the Algebraic Theory of Quadratic Forms

Geometric Methods in the Algebraic Theory of Quadratic Forms
Author: Oleg T. Izhboldin
Publisher: Springer
Total Pages: 198
Release: 2004-02-07
Genre: Mathematics
ISBN: 3540409904
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The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.

Effective Methods in Algebraic Geometry

Effective Methods in Algebraic Geometry
Author: Teo Mora
Publisher: Springer Science & Business Media
Total Pages: 524
Release: 1991
Genre: Mathematics
ISBN: 9780817635466
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On Lack of Effectiveness in Semi-algebraic Geometry.- A simple constructive proof of Canonical Resolution of Singularities.- Local Membership Problems for Polynomial Ideals.- Un Algorithme pour le Calcul des Résultants.- On algorithms for real algebraic plane curves.- Duality methods for the membership problem.- Exemples d'ensembles de Points en Position Uniforme.- Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets.- Noetherian Properties and Growth of some Associative Algebras.- Codes and Elliptic Curves.- Algorithmes - disons rapides - pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles.- Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators.- Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals.- On the Complexity of Zero-dimensional Algebraic Systems.- A Single Exponential Bound on the Complexity of Computing Gröbner Bases of Zero Dimensional Ideals.- Algorithms for a Multiple Algebraic Extension.- Elementary constructive theory of ordered fields.- Effective real Nullstellensatz and variants.- Algorithms for the Solution of Systems of Linear Equations in Commutative Rings.- Une conjecture sur les anneaux de Chow A(G, ?) renforcée par un calcul formel.- Construction de courbes de genre 2 à partir de leurs modules.- Computing Syzygies à la Gau?-Jordan.- The non-scalar Model of Complexity in Computational Geometry.- Géométrie et Interpretations Génériques, un Algorithme.- Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms.- The tangent cone algorithm and some applications to local algebraic geometry.- Effective Methods for Systems of Algebraic Partial Differential Equations.- Finding roots of equations involving functions defined by first order algebraic differential equations.- Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties.- Sign determination on zero dimensional sets.- A Classification of Finite-dimensional Monomial Algebras.- An algorithm related to compactifications of adjoint groups.- Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time.

Algebraic and Geometric Methods in Statistics

Algebraic and Geometric Methods in Statistics
Author: Paolo Gibilisco
Publisher: Cambridge University Press
Total Pages: 447
Release: 2010
Genre: Mathematics
ISBN: 0521896193
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An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.

Algebraic Geometry and Number Theory

Algebraic Geometry and Number Theory
Author: victor ginzburg
Publisher: Springer Science & Business Media
Total Pages: 656
Release: 2007-12-31
Genre: Mathematics
ISBN: 0817645322
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This book represents a collection of invited papers by outstanding mathematicians in algebra, algebraic geometry, and number theory dedicated to Vladimir Drinfeld. Original research articles reflect the range of Drinfeld's work, and his profound contributions to the Langlands program, quantum groups, and mathematical physics are paid particular attention. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory.

Geometric Methods and Applications

Geometric Methods and Applications
Author: Jean Gallier
Publisher: Springer Science & Business Media
Total Pages: 584
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461301378
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As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

Algebraic and Geometric Methods in Nonlinear Control Theory

Algebraic and Geometric Methods in Nonlinear Control Theory
Author: M. Fliess
Publisher: Springer Science & Business Media
Total Pages: 630
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400947062
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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point"of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras ·are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Geometrical Methods for the Theory of Linear Systems

Geometrical Methods for the Theory of Linear Systems
Author: C.I. Byrnes
Publisher: Springer Science & Business Media
Total Pages: 320
Release: 2012-12-06
Genre: Science
ISBN: 9400990820
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The lectures contained in this book were presented at Harvard University in June 1979. The workshop at which they were presented was the third such on algebro-geometric methods. The first was held in 1973 in London and the emphasis was largely on geometric methods. The second was held at Ames Research Center-NASA in 1976. There again the emphasis was on geometric methods, but algebraic geometry was becoming a dominant theme. In the two years after the Ames meeting there was tremendous growth in the applications of algebraic geometry to systems theory and it was becoming clear that much of the algebraic systems theory was very closely related to the geometric systems theory. On this basis we felt that this was the right time to devote a workshop to the applications of algebra and algebraic geometry to linear systems theory. The lectures contained in this volume represent all but one of the tutorial lectures presented at the workshop. The lec ture of Professor Murray Wonham is not contained in this volume and we refer the interested to the archival literature. This workshop was jointly sponsored by a grant from Ames Research Center-NASA and a grant from the Advanced Study Institute Program of NATO. We greatly appreciate the financial support rendered by these two organizations. The American Mathematical Society hosted this meeting as part of their Summer Seminars in Applied Mathematics and will publish the companion volume of con tributed papers.