Applications of Algebraic Geometry to Coding Theory, Physics and Computation (NATO Science Series II: Mathematics, Physics and Chemistry)

Cover of: Applications of Algebraic Geometry to Coding Theory, Physics and Computation (NATO Science Series II: Mathematics, Physics and Chemistry) |

Published by Springer .

Written in English

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Subjects:

  • Algebraic Geometry,
  • Geometry - Algebraic,
  • Mathematics,
  • Science/Mathematics,
  • Geometry, Algebraic,
  • Computer Science,
  • General,
  • Computers-Computer Science,
  • Mathematics / Geometry / Algebraic,
  • Medical-General,
  • Congresses

Edition Notes

Book details

ContributionsCiro Ciliberto (Editor), Friedrich Hirzebruch (Editor), Rick Miranda (Editor), Mina Teicher (Editor)
The Physical Object
FormatHardcover
Number of Pages360
ID Numbers
Open LibraryOL8369695M
ISBN 101402000049
ISBN 109781402000041

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Buy Applications of Algebraic Geometry to Coding Theory, Physics and Computation (Nato Science Series II:) on FREE SHIPPING on qualified orders Applications of Algebraic Geometry to Coding Theory, Physics and Computation (Nato Science Series II:): Ciro Ciliberto, Friedrich Hirzebruch, Rick Miranda, Mina Teicher: Amazon.

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.

Main Applications of Algebraic Geometry to Coding Theory, Physics and Computation Due to the technical work on the site downloading books (as well as file conversion and sending books to email/kindle) may be unstable from May, 27 to May, 28 Also, for users who have an active donation now, we will extend the donation period.

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.

between arithmetic geometry and its applications, originally highlighting coding theory but more recently including cryptography and other areas as well.

This volume contains the proceedings of the 16th international conference, held from. Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents Physics and Computation book group research completed for the February conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM).

Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular.

This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these : Brendan Hassett.

We develop the basic theory of toric dynamical systems in the context of computational algebraic geometry and show that the associated moduli space is also a toric : Tony Shaska. Applications of Linear Algebra to Coding Theory Presented by: t kaur Dept of Mathematics SIES (W) • International Standard Book Number (ISBN) Coding Theory Vs Cryptography • Coding theory deals Applications of Linear Algebra to Coding Theory.

This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in : $ About this book Introduction 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.

Chapter book in 'Applications of Algebraic Geometry to Coding Theory, Physics and Computation' Subjects: Algebraic Geometry (); Information Theory () Cite as: arXiv:math/ [] (or arXiv:math/v1 [] for this version)Cited by: 1.

Computational algebraic geometry today 65 M. Fryers, J.Y. Kaminski and M. Teicher: Some applications of algebraic curves to computational vision G.

van der Geer: Coding theory and algebraic curves over finite fields G.-M. Greuel, C. Lossen and M. Schulze: Three algorithms in algebraic geometry, coding theory and singularity theOlYFile Size: KB. Get this from a library. Applications of algebraic geometry to coding theory, physics, and computation.

[C Ciliberto;]. Complex projective spaces show up quite a bit. As far as an algebraic geometer is concerned, these are probably the most fundamental and elementary objects in their field, but at the end of the day it is still algebraic geometry.

The study of co. Coding Theory and Algebraic Geometry, Mathematics and its Applications,Dordrecht: Priti Shankar ( words) [view diff] exact match in snippet view article find links to article the areas of compiler design, formal language theory and algorithmic coding theory.

APPLICATIONS OF ALGEBRAIC GEOMETRY TO CODING THEORY, PHYSICS AND COMPUTATION (NATO SCIENCE SERIES II:) by HIRZEBRUCH, FRIEDRICH (EDITOR) and a great selection of related books, art and collectibles available now at B. Szendröi, Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry, ``Applications of Algebraic Geometry to Coding Theory, Physics and Computation'', NATO Science Series Kluwer () A.N.

Todorov, Application of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surface, Invent. Math. 61 () The Segre and Harbourne-Hirschowitz Conjectures, in: Applications of algebraic geometry to coding theory, physics and computation (Eilat ).

Get this from a library. Applications of Algebraic Geometry to Coding Theory, Physics and Computation. [Ciro Ciliberto; Friedrich Hirzebruch; Rick Miranda; Mina Teicher] -- 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.

topics in algebraic coding theory Download topics in algebraic coding theory or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get topics in algebraic coding theory book now. This site is like a library, Use search box.

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 : $ Why Algebraic Geometry.

Although the general theory of linear codes is well established, a number of computational problems central to coding theory, such as decoding and the determination of minimum distances, are known to be NP-Complete, see([12],98).

There is no known "efficient" algorithm for solving any of the NP-Complete problems. In this thesis, we develop a geometric foundation for classical coding over fields and commutative rings using modern algebraic geometry and the language of schemes.

Using this framework we construct an equivalence between the category of geometric linear codes over Spec k and linear codes over k. We also study the minimum distance properties of codes under base changes and localizations.

The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched.

[citation needed]Algebraic coding theory is basically divided into two major types of codes: [citation needed] Linear block codes; Convolutional codes; It analyzes the following three properties of a code – mainly: [citation needed]. Griffiths and Harris' "Principles of Algebraic Geometry" (Wiley) is the best for your purposes (read only the parts on Kahler geometry).

The sections on algebraic geometry in "Mirror Symmetry" (Clay/AMS) are essentially a Crib Notes version of that paper and some of the classic CY and special geometry papers referred to above.

Read the latest articles of Journal of Symbolic Computation atElsevier’s leading platform of peer-reviewed scholarly literature Special issue algebraic coding theory and applications.

Antonio Campillo, Patrick Fitzpatrick, Edgar Martínez-Moro, Ruud Pellikaan. select article Algebraic geometry codes from polyhedral. Algebra and Discrete Mathematics (Deadline: 20 December ) Group Theory and Related Topics (Deadline: 31 December ) New Insights in Algebra, Discrete Mathematics, and Number Theory (Deadline: 31 January ) New Trends in Algebraic Geometry and Its Applications (Deadline: 31 January ).

Here's an example of a ``real-life'' application of algebraic geometry. Consider an optimal control problem that adheres to the Karush-Kuhn-Tucker criteria and is completely polynomial in nature (being completely polynomial is not absolutely necessary to find solutions, but it is to find a global solution).

This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance.

and algebraic coding theory. The lectures in the book. Applications of Algebraic Geometry to Coding Theory, Physics and Computation Kaina internetu: ,39 €. Dear Colleagues, Combinatorial algebraic geometry is a branch of mathematics studying objects that can be interpreted from a combinatorial point of view (such as matroids, polytopes, codes or finite geometries) and also algebraically (using tools from group theory, lattice theory or commutative algebra), and which has applications in designs, coding theory, cryptography, and number theory.

I would love to see some examples of applications of topology or algebraic topology to getting actual results or concepts clarified in physics. One example I always here is "K-theory is the proper receptacle for charge" and maybe someone could start by elaborating on that.

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of.

Course Notes on Coding Theory. This note covers the following topics: Basic codes and constructions, Algebraic Geometry Codes, Limits on Performance of Codes, Algebraic decoding, Algebraic decoding, Linear time decoding, Decoding from random errors and erasures, Applications in complexity theory and Complexity results in coding theory.

Abstract: This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more.

It's century old algebraic geometry, but it's still algebraic geometry. $\endgroup$ – bubba Oct 15 '13 at $\begingroup$ Certainly, learning why vector bundles and moduli spaces are useful in physics would be a good start, though I'm afraid I don't know enough about physics to give you good references for that.

$\endgroup$ – user   Commutative Algebra, Algebraic Geometry, Number theory, Field Theory, Galois Theory by Sudhir R. Ghorpade Fundamental Problems in Algorithmic Algebra by Chee Yap Braid groups and Galois theory by Author: Kevin de Asis. Quantum Algebraic-Geometric Codes Chiu Fan Lee Clare Hall Cambridge 2 Review on coding theory 3 This essay aims to discuss the application of algebraic geometry on quantum error-correcting codes.

The motivation behind is the potential error-correcting. It explicitly states that it discusses algebraic topology but doesn't make any statement about algebraic geometry. But there are books on algebraic geometry in its references section. Also I don't think a book covering that much things and also discussing bosonic string theory, omits algebraic geometry.Some of the topics planned for discussion include algebraic cryptanalysis and coding theory, chemical reaction networks, computational biology, computer-aided geometric design, applications of enumerative and tropical geometry, gauge and string theory in physics, and applications to statistics such as probabilistic graphical models and singular.The foundation of algebraic geometry is the solving of systems of polynomial equations.

When the equations to be considered are defined over a subfield of the complex numbers, numerical methods can be used to perform algebraic geometric computations forming the area of numerical algebraic by: 9.

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