Emerging Applications Of Algebraic Geometry

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Emerging Applications of Algebraic Geometry

Mihai Putinar,Seth Sullivant
Emerging Applications of Algebraic Geometry Book PDF

Author : Mihai Putinar,Seth Sullivant
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 53,6 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9780387096865

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Emerging Applications of Algebraic Geometry by Mihai Putinar,Seth Sullivant Pdf

Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.

Using Algebraic Geometry

David A. Cox,John Little,DONAL OSHEA
Using Algebraic Geometry Book PDF

Author : David A. Cox,John Little,DONAL OSHEA
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 44,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475769111

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Using Algebraic Geometry by David A. Cox,John Little,DONAL OSHEA Pdf

An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

SAGA – Advances in ShApes, Geometry, and Algebra

Tor Dokken,Georg Muntingh
SAGA Advances in ShApes Geometry and Algebra Book PDF

Author : Tor Dokken,Georg Muntingh
Publisher : Springer
Page : 323 pages
File Size : 44,5 Mb
Release : 2014-10-24
Category : Mathematics
ISBN : 9783319086354

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SAGA – Advances in ShApes, Geometry, and Algebra by Tor Dokken,Georg Muntingh Pdf

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

Computations in Algebraic Geometry with Macaulay 2

David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Computations in Algebraic Geometry with Macaulay 2 Book PDF

Author : David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 49,6 Mb
Release : 2001-09-25
Category : Mathematics
ISBN : 3540422307

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Computations in Algebraic Geometry with Macaulay 2 by David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels Pdf

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Using Algebraic Geometry

David A. Cox,John Little,Donal O'Shea
Using Algebraic Geometry Book PDF

Author : David A. Cox,John Little,Donal O'Shea
Publisher : Springer Science & Business Media
Page : 582 pages
File Size : 46,8 Mb
Release : 2005-11-23
Category : Mathematics
ISBN : 9780387271057

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Using Algebraic Geometry by David A. Cox,John Little,Donal O'Shea Pdf

The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout.

Semidefinite Optimization and Convex Algebraic Geometry

Grigoriy Blekherman,Pablo A. Parrilo,Rekha R. Thomas
Semidefinite Optimization and Convex Algebraic Geometry Book PDF

Author : Grigoriy Blekherman,Pablo A. Parrilo,Rekha R. Thomas
Publisher : SIAM
Page : 487 pages
File Size : 47,5 Mb
Release : 2013-03-21
Category : Mathematics
ISBN : 9781611972283

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Semidefinite Optimization and Convex Algebraic Geometry by Grigoriy Blekherman,Pablo A. Parrilo,Rekha R. Thomas Pdf

An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

Algebraic Geometry and its Applications

Chandrajit L. Bajaj
Algebraic Geometry and its Applications Book PDF

Author : Chandrajit L. Bajaj
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461226284

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Algebraic Geometry and its Applications by Chandrajit L. Bajaj Pdf

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.

Geometry, Algebra, Number Theory, and Their Information Technology Applications

Amir Akbary,Sanoli Gun
Geometry Algebra Number Theory and Their Information Technology Applications Book PDF

Author : Amir Akbary,Sanoli Gun
Publisher : Springer
Page : 528 pages
File Size : 44,6 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9783319973791

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Geometry, Algebra, Number Theory, and Their Information Technology Applications by Amir Akbary,Sanoli Gun Pdf

This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties The emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.

Cohomological and Geometric Approaches to Rationality Problems

Fedor Bogomolov,Yuri Tschinkel
Cohomological and Geometric Approaches to Rationality Problems Book PDF

Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 45,7 Mb
Release : 2009-11-03
Category : Mathematics
ISBN : 9780817649340

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Cohomological and Geometric Approaches to Rationality Problems by Fedor Bogomolov,Yuri Tschinkel Pdf

Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov

Arithmetic Algebraic Geometry

G., van der Geer,F. Oort,J.H.M. Steenbrink
Arithmetic Algebraic Geometry Book PDF

Author : G., van der Geer,F. Oort,J.H.M. Steenbrink
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204572

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Arithmetic Algebraic Geometry by G., van der Geer,F. Oort,J.H.M. Steenbrink Pdf

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.

New Scientific Applications of Geometry and Topology

De Witt L. Sumners,Nicholas R. Cozzarelli
New Scientific Applications of Geometry and Topology Book PDF

Author : De Witt L. Sumners,Nicholas R. Cozzarelli
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 46,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855026

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New Scientific Applications of Geometry and Topology by De Witt L. Sumners,Nicholas R. Cozzarelli Pdf

Geometry and topology are subjects generally considered to be "pure" mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.

New Trends in Algebraic Geometry and Its Applications

Sonia P ́erez-D ́ıaz
New Trends in Algebraic Geometry and Its Applications Book PDF

Author : Sonia P ́erez-D ́ıaz
Publisher : Mdpi AG
Page : 188 pages
File Size : 43,7 Mb
Release : 2021-10-29
Category : Technology & Engineering
ISBN : 3036523073

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New Trends in Algebraic Geometry and Its Applications by Sonia P ́erez-D ́ıaz Pdf

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.

Software for Algebraic Geometry

Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Software for Algebraic Geometry Book PDF

Author : Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 44,6 Mb
Release : 2008-05-29
Category : Mathematics
ISBN : 9780387781334

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Software for Algebraic Geometry by Michael E. Stillman,Nobuki Takayama,Jan Verschelde Pdf

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.

Algorithms in Algebraic Geometry

Alicia Dickenstein,Frank-Olaf Schreyer,Andrew J. Sommese
Algorithms in Algebraic Geometry Book PDF

Author : Alicia Dickenstein,Frank-Olaf Schreyer,Andrew J. Sommese
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 44,7 Mb
Release : 2010-07-10
Category : Mathematics
ISBN : 9780387751559

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Algorithms in Algebraic Geometry by Alicia Dickenstein,Frank-Olaf Schreyer,Andrew J. Sommese Pdf

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 2006 is one tangible indication of the interest. This volume of articles captures some of the spirit of the IMA workshop.

Numerical Semigroups and Applications

Abdallah Assi,Marco D'Anna,Pedro A. García-Sánchez
Numerical Semigroups and Applications Book PDF

Author : Abdallah Assi,Marco D'Anna,Pedro A. García-Sánchez
Publisher : Springer Nature
Page : 138 pages
File Size : 43,9 Mb
Release : 2020-10-01
Category : Mathematics
ISBN : 9783030549435

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Numerical Semigroups and Applications by Abdallah Assi,Marco D'Anna,Pedro A. García-Sánchez Pdf

This book is an extended and revised version of "Numerical Semigroups with Applications," published by Springer as part of the RSME series. Like the first edition, it presents applications of numerical semigroups in Algebraic Geometry, Number Theory and Coding Theory. It starts by discussing the basic notions related to numerical semigroups and those needed to understand semigroups associated with irreducible meromorphic series. It then derives a series of applications in curves and factorization invariants. A new chapter is included, which offers a detailed review of ideals for numerical semigroups. Based on this new chapter, descriptions of the module of Kähler differentials for an algebroid curve and for a polynomial curve are provided. Moreover, the concept of tame degree has been included, and is viewed in relation to other factorization invariants appearing in the first edition. This content highlights new applications of numerical semigroups and their ideals, following in the spirit of the first edition.