Real Algebraic Geometry And Ordered Structures
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| Author | : Charles N. Delzell |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 320 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821808044 |
This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.
| Author | : Michel Coste |
| Publisher | : Springer |
| Total Pages | : 425 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540473378 |
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.
| Author | : Saugata Basu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 602 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662053551 |
In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
| Author | : Gregory W. Brumfiel |
| Publisher | : Cambridge University Press |
| Total Pages | : 293 |
| Release | : 1979-12-20 |
| Genre | : Mathematics |
| ISBN | : 052122845X |
The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance.
| Author | : Fabrizio Broglia |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 390 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 1470429667 |
Contains the proceedings of the international conference "Ordered Algebraic Structures and Related Topics", held in October 2015, at CIRM, Luminy, Marseilles. Papers cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.
| Author | : Bill Jacob |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 416 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821851543 |
The papers collected here present an up-to-date record of the current research developments in the fields of real algebraic geometry and quadratic forms. Articles range from the technical to the expository and there are also indications to new research directions.
| Author | : Paulo Ribenboim |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2020-01-17 |
| Genre | : Mathematics |
| ISBN | : 9783319721439 |
This two-volume collection contains Paulo Ribenboim’s work on ordered structures and mathematical logic. Two long unpublished papers and a reproduction of his first book on abelian groups are also featured in these volumes. With over 240 publications, including 13 books, Ribenboim is responsible for some of the most influential research in number theory, mathematical logic, and algebraic structures. Together, these volumes include papers on algebraic structures on directed graphs, real algebraic geometry, applications of model theory in collaboration with Lou van den Dries, and more recent papers with Sibylla Priess-Crampe on mathematical logic programming and Ultrametric spaces. The Ribenboim Prize of the Canadian Number Theory Association is named after him. Paulo Ribenboim is currently professor emeritus at Queen’s University in Kingston, Ontario.
| Author | : Salma Kuhlmann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 186 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821809431 |
Model theoretic algebra has witnessed remarkable progress in the last few years. It has found profound applications in other areas of mathematics, notably in algebraic geometry and in singularity theory. Since Wilkie's results on the o-minimality of the expansion of the reals by the exponential function, and most recently even by all Pfaffian functions, the study of o-minimal expansions of the reals has become a fascinating topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research. Through the Artin-Schreier Theory of real closed fields, the structure of the non-archimedean models in the semi-algebraic case is well understood. For the o-minimal case, so far there has been no systematic study of the non-archimedean models. The goal of this monograph is to serve this purpose. The author presents a detailed description of the non-archimedean models of the elementary theory of certain o-minimal expansions of the reals in which the exponential function is definable. The example of exponential Hardy fields is worked out with particular emphasis. The basic tool is valuation theory, and a sufficient amount of background material on orderings and valuations is presented for the convenience of the reader.
| Author | : Robin Hartshorne |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 511 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475738498 |
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
| Author | : Gregory Budzban |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821820273 |
This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.
