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Author : A. Hamid A. Hussain Ali
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (23 download)
Download or read book Some Aspects of the Jacobian Conjecture written by A. Hamid A. Hussain Ali and published by . This book was released on 1987 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Hamid A. Hussain Ali
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (23 download)
Download or read book Some Aspects of the Jacobian Conjecture written by A. Hamid A. Hussain Ali and published by . This book was released on 1987 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arno van den Essen
Publisher : Springer Science & Business Media
ISBN 13 : 9783764363505
Total Pages : 360 pages
Book Rating : 4.3/5 (635 download)
Download or read book Polynomial Automorphisms written by Arno van den Essen and published by Springer Science & Business Media. This book was released on 2000-09 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.
Author : Arno van den Essen
Publisher : Birkhäuser
ISBN 13 : 3034884400
Total Pages : 336 pages
Book Rating : 4.0/5 (348 download)
Download or read book Polynomial Automorphisms written by Arno van den Essen and published by Birkhäuser. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.
Author : Edward Formanek
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (11 download)
Download or read book Observations about the Jacobian Conjecture written by Edward Formanek and published by . This book was released on 1993 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : S. C. Coutinho
Publisher : Cambridge University Press
ISBN 13 : 0521551196
Total Pages : 223 pages
Book Rating : 4.5/5 (215 download)
Download or read book A Primer of Algebraic D-Modules written by S. C. Coutinho and published by Cambridge University Press. This book was released on 1995-09-07 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.
Author : Arno van den Essen
Publisher : Springer Nature
ISBN 13 : 3030605353
Total Pages : 197 pages
Book Rating : 4.0/5 (36 download)
Download or read book Polynomial Automorphisms and the Jacobian Conjecture written by Arno van den Essen and published by Springer Nature. This book was released on 2021-03-31 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000. Many new exciting results have been obtained in the past two decades, including the solution of Nagata's Conjecture, the complete solution of Hilbert's fourteenth problem, the equivalence of the Jacobian Conjecture and the Dixmier Conjecture, the symmetric reduction of the Jacobian Conjecture, the theory of Mathieu-Zhao spaces and counterexamples to the Cancellation problem in positive characteristic. These and many more results are discussed in detail in this work. The book is aimed at graduate students and researchers in the field of Affine Algebraic Geometry. Exercises are included at the end of each section.
Author : Arnoldus Richardus Petrus van den Essen
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (463 download)
Download or read book Conjectures and Problems Surrounding the Jacobian Conjecture written by Arnoldus Richardus Petrus van den Essen and published by . This book was released on 1993 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrew Richard Booker
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (45 download)
Download or read book The Jacobian Conjecture written by Andrew Richard Booker and published by . This book was released on 1998 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter Woit
Publisher : Springer
ISBN 13 : 3319646125
Total Pages : 659 pages
Book Rating : 4.3/5 (196 download)
Download or read book Quantum Theory, Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Author : Zhi-Li Zhang
Publisher :
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4.:/5 (3 download)
Download or read book A Note on the Jacobian Conjecture written by Zhi-Li Zhang and published by . This book was released on 1990 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Stefanescu
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (551 download)
Download or read book On the Jacobian Conjecture written by D. Stefanescu and published by . This book was released on 1986 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bjorn Poonen
Publisher : American Mathematical Society
ISBN 13 : 1470474581
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Society. This book was released on 2023-08-10 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere. The origins of arithmetic (or Diophantine) geometry can be traced back to antiquity, and it remains a lively and wide research domain up to our days. The book by Bjorn Poonen, a leading expert in the field, opens doors to this vast field for many readers with different experiences and backgrounds. It leads through various algebraic geometric constructions towards its central subject: obstructions to existence of rational points. —Yuri Manin, Max-Planck-Institute, Bonn It is clear that my mathematical life would have been very different if a book like this had been around at the time I was a student. —Hendrik Lenstra, University Leiden Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics. —Jean-Louis Colliot-Thélène, Université Paris-Sud A beautiful subject, handled by a master. —Joseph Silverman, Brown University
Author : Alexander Mikhalev
Publisher : Springer Science & Business Media
ISBN 13 : 9780387405629
Total Pages : 336 pages
Book Rating : 4.4/5 (56 download)
Download or read book Combinatorial Methods written by Alexander Mikhalev and published by Springer Science & Business Media. This book was released on 2004 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century. This book is divided into three fairly independent parts. Part I provides a brief exposition of several classical techniques in combinatorial group theory, namely, methods of Nielsen, Whitehead, and Tietze. Part II contains the main focus of the book. Here the authors show how the aforementioned techniques of combinatorial group theory found their way into affine algebraic geometry, a fascinating area of mathematics that studies polynomials and polynomial mappings. Part III illustrates how ideas from combinatorial group theory contributed to the theory of free algebras. The focus here is on Schreier varieties of algebras (a variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras).
Author : Mee Seong Im
Publisher : American Mathematical Society
ISBN 13 : 1470470349
Total Pages : 240 pages
Book Rating : 4.4/5 (74 download)
Download or read book Algebraic and Topological Aspects of Representation Theory written by Mee Seong Im and published by American Mathematical Society. This book was released on 2024-01-22 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20–21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.
Author : William J. L. Adams
Publisher :
ISBN 13 :
Total Pages : 80 pages
Book Rating : 4.:/5 (382 download)
Download or read book A Personal Tour of the Jacobian Conjecture written by William J. L. Adams and published by . This book was released on 1997 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John W. Morgan
Publisher : American Mathematical Soc.
ISBN 13 : 9780821843284
Total Pages : 586 pages
Book Rating : 4.8/5 (432 download)
Download or read book Ricci Flow and the Poincare Conjecture written by John W. Morgan and published by American Mathematical Soc.. This book was released on 2007 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
