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Author: Sonia P ́erez-D ́ıaz Publisher: Mdpi AG ISBN: 9783036523071 Category : Technology & Engineering Languages : en Pages : 188
Book Description
Unirrational algebraic varieties, particularly curves and surfaces, play an important role in many fields, such as Algebraic Geometry, Computational Geometry, Computer-Aided Design, Computer Graphics, and Geometric Modeling. Consequently, algorithms and results dealing with the different algebraic and geometric problems involving these geometric objects are very important. This Special Issue on "New Trends in Algebraic Geometry and Its Applications" is directed at mathematicians and computer scientists with a particular interest in algebraic geometry and its applications. This Special Issue aims to facilitate communication between researchers addressing the fundamental algorithmic issues in the treatment of curves and surfaces (from symbolic and numeric perspectives). The contributions presented in this Special Issue explore the interplay between geometry, algebra, and numerical computation when designing a variety of algorithms, or provide a complexity analysis of the running time of such algorithms. This Special Issue focuses on recent problems concerning algebraic geometry and its applications as an algorithm for visualizing algebraic varieties, in scientific and computational algebra, computational and algebraic geometry, and computer algebra problems, solved by means of symbolic-numeric techniques.
Author: Sonia P ́erez-D ́ıaz Publisher: Mdpi AG ISBN: 9783036523071 Category : Technology & Engineering Languages : en Pages : 188
Book Description
Unirrational algebraic varieties, particularly curves and surfaces, play an important role in many fields, such as Algebraic Geometry, Computational Geometry, Computer-Aided Design, Computer Graphics, and Geometric Modeling. Consequently, algorithms and results dealing with the different algebraic and geometric problems involving these geometric objects are very important. This Special Issue on "New Trends in Algebraic Geometry and Its Applications" is directed at mathematicians and computer scientists with a particular interest in algebraic geometry and its applications. This Special Issue aims to facilitate communication between researchers addressing the fundamental algorithmic issues in the treatment of curves and surfaces (from symbolic and numeric perspectives). The contributions presented in this Special Issue explore the interplay between geometry, algebra, and numerical computation when designing a variety of algorithms, or provide a complexity analysis of the running time of such algorithms. This Special Issue focuses on recent problems concerning algebraic geometry and its applications as an algorithm for visualizing algebraic varieties, in scientific and computational algebra, computational and algebraic geometry, and computer algebra problems, solved by means of symbolic-numeric techniques.
Author: Klaus Hulek Publisher: Cambridge University Press ISBN: 9780521646598 Category : Mathematics Languages : en Pages : 500
Book Description
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.
Author: Luciano Boi Publisher: World Scientific ISBN: 1848166435 Category : Mathematics Languages : en Pages : 329
Book Description
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.
Author: Raffaele de Amicis Publisher: Springer ISBN: 144716461X Category : Mathematics Languages : en Pages : 166
Book Description
Mathematical algorithms are a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between algebraic geometry and geometric modelling algorithms, formulated within a computer science framework. Apart from the algebraic geometry topics covered, the entire book is based on the unifying concept of using algebraic techniques – properly specialized to solve geometric problems – to seriously improve accuracy, robustness and efficiency of CAD-systems. It provides new approaches as well as industrial applications to deform surfaces when animating virtual characters, to automatically compare images of handwritten signatures and to improve control of NC machines. This book further introduces a noteworthy representation based on 2D contours, which is essential to model the metal sheet in industrial processes. It additionally reviews applications of numerical algebraic geometry to differential equations systems with multiple solutions and bifurcations. Future Vision and Trends on Shapes, Geometry and Algebra is aimed specialists in the area of mathematics and computer science on the one hand and on the other hand at those who want to become familiar with the practical application of algebraic geometry and geometric modelling such as students, researchers and doctorates.
Author: Robert Rolland Publisher: World Scientific ISBN: 9814471666 Category : Mathematics Languages : en Pages : 530
Book Description
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.
Author: Michael E. Stillman Publisher: Springer Science & Business Media ISBN: 0387781331 Category : Mathematics Languages : en Pages : 176
Book Description
Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop “Software for Algebraic Geometry” held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.
Author: Chandrajit L. Bajaj Publisher: Springer Science & Business Media ISBN: 1461226287 Category : Mathematics Languages : en Pages : 530
Book Description
Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.-P. Serre.
Author: Ciro Ciliberto Publisher: Springer Science & Business Media ISBN: 9401010110 Category : Mathematics Languages : en Pages : 343
Book Description
An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.
Author: Sonia P ́erez-D ́ıaz
Author: Sonia P ́erez-D ́ıaz
Author: Klaus Hulek
Author: Luciano Boi
Author: Raffaele de Amicis
Author: Lucia Caporaso
Author: Robert Rolland
Author: Sergeĭ Mikhaĭlovich Nikolʹskiĭ
Author: Michael E. Stillman
Author: Chandrajit L. Bajaj
Author: Ciro Ciliberto