New Trends In Algebraic Geometry And Its Applications

Author : Sonia P ́erez-D ́ıaz
Publisher : Mdpi AG
Page : 188 pages
File Size : 44,5 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.

Author : Klaus Hulek
Publisher : Cambridge University Press
Page : 500 pages
File Size : 50,6 Mb
Release : 1999-05-13
Category : Mathematics
ISBN : 0521646596

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New Trends in Algebraic Geometry by Klaus Hulek Pdf

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 : Raffaele Amicis,Giuseppe Conti
Publisher : Unknown
Page : 172 pages
File Size : 53,8 Mb
Release : 2014-07-31
Category : Electronic
ISBN : 1447164628

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Future Vision and Trends on Shapes, Geometry and Algebra by Raffaele Amicis,Giuseppe Conti Pdf

Author : Lucia Caporaso
Publisher : Cambridge University Press
Page : 437 pages
File Size : 50,9 Mb
Release : 2012-03-19
Category : Mathematics
ISBN : 9780521768252

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Current Developments in Algebraic Geometry by Lucia Caporaso Pdf

This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.

Author : Sergeĭ Mikhaĭlovich Nikolʹskiĭ,E. A. Volkov
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 50,5 Mb
Release : 1986
Category : Mathematics
ISBN : 0821830929

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Algebraic Geometry and Its Applications by Sergeĭ Mikhaĭlovich Nikolʹskiĭ,E. A. Volkov Pdf

Papers about algebraic geometry and their applications.

Author : Shiing-Shen Chern,Lei Fu,Richard Martin Hain
Publisher : World Scientific
Page : 276 pages
File Size : 48,8 Mb
Release : 2002
Category : Mathematics
ISBN : 9789810249540

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Contemporary Trends in Algebraic Geometry and Algebraic Topology by Shiing-Shen Chern,Lei Fu,Richard Martin Hain Pdf

The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics. It was devoted to memorializing those two outstanding and original Chinese mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st Century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, etc.This invaluable volume contains the selected papers presented at the conference. The topics include canonical maps of Gorenstein 3-folds, fundamental groups of algebraic curves, Chen's interated integrals, algebraic fiber spaces, and others.

Author : Luchezar L. Avramov,Mark Green,Craig Huneke,Karen E. Smith,Bernd Sturmfels
Publisher : Cambridge University Press
Page : 7 pages
File Size : 51,6 Mb
Release : 2004-12-13
Category : Mathematics
ISBN : 9780521831956

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Trends in Commutative Algebra by Luchezar L. Avramov,Mark Green,Craig Huneke,Karen E. Smith,Bernd Sturmfels Pdf

This book describes the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology, and combinatorics.

Author : Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 46,5 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.

Author : Igor V. Nikolaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 276 pages
File Size : 42,6 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783110545258

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Noncommutative Geometry by Igor V. Nikolaev Pdf

This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. Contents Part I: Basics Model examples Categories and functors C∗-algebras Part II: Noncommutative invariants Topology Algebraic geometry Number theory Part III: Brief survey of NCG Finite geometries Continuous geometries Connes geometries Index theory Jones polynomials Quantum groups Noncommutative algebraic geometry Trends in noncommutative geometry

Author : Miles Reid,Alexei Skorobogatov
Publisher : Cambridge University Press
Page : 312 pages
File Size : 42,9 Mb
Release : 2003
Category : Mathematics
ISBN : 0521545188

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Number Theory and Algebraic Geometry by Miles Reid,Alexei Skorobogatov Pdf

This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.

Author : Hélène Barcelo,Gizem Karaali,Rosa Orellana
Publisher : Springer
Page : 362 pages
File Size : 54,9 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030051419

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Recent Trends in Algebraic Combinatorics by Hélène Barcelo,Gizem Karaali,Rosa Orellana Pdf

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.

Author : Nicolás Andruskiewitsch,Walter Ricardo Ferrer Santos,Hans-Jürgen Schneider
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 55,9 Mb
Release : 2000
Category : Hopf algebras
ISBN : 9780821821268

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New Trends in Hopf Algebra Theory by Nicolás Andruskiewitsch,Walter Ricardo Ferrer Santos,Hans-Jürgen Schneider Pdf

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.

Author : Frank Neumann,Ambrus Pál
Publisher : Springer Nature
Page : 223 pages
File Size : 45,9 Mb
Release : 2021-09-29
Category : Mathematics
ISBN : 9783030789770

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Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects by Frank Neumann,Ambrus Pál Pdf

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.

Author : J. Madore
Publisher : Cambridge University Press
Page : 381 pages
File Size : 52,9 Mb
Release : 1999-06-24
Category : Mathematics
ISBN : 9780521659918

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An Introduction to Noncommutative Differential Geometry and Its Physical Applications by J. Madore Pdf

A thoroughly revised introduction to non-commutative geometry.

Author : Mark E. Mahowald
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 52,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821808054

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Homotopy Theory via Algebraic Geometry and Group Representations by Mark E. Mahowald Pdf

The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.