Real Algebraic Geometry and Ordered Structures

by Charles N. Delzell

Author	: Charles N. Delzell
Publisher	: American Mathematical Soc.
Total Pages	: 320
Release	: 2000
Genre	: Mathematics
ISBN	: 0821808044

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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.

Real Algebraic Geometry

by Michel Coste

Author	: Michel Coste
Publisher	: Springer
Total Pages	: 425
Release	: 2006-11-15
Genre	: Mathematics
ISBN	: 3540473378

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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.

Algorithms in Real Algebraic Geometry

by Saugata Basu

Author	: Saugata Basu
Publisher	: Springer Science & Business Media
Total Pages	: 602
Release	: 2013-03-09
Genre	: Mathematics
ISBN	: 3662053551

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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.

Partially Ordered Rings and Semi-Algebraic Geometry

by Gregory W. Brumfiel

Author	: Gregory W. Brumfiel
Publisher	: Cambridge University Press
Total Pages	: 293
Release	: 1979-12-20
Genre	: Mathematics
ISBN	: 052122845X

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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.

Collected Works in Ordered Structures and Mathematical Logic

by Paulo Ribenboim

Author	: Paulo Ribenboim
Publisher	: Springer
Total Pages	: 0
Release	: 2020-01-17
Genre	: Mathematics
ISBN	: 9783319721439

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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.

Ordered Algebraic Structures and Related Topics

by Fabrizio Broglia

Author	: Fabrizio Broglia
Publisher	: American Mathematical Soc.
Total Pages	: 390
Release	: 2017
Genre	: Mathematics
ISBN	: 1470429667

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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.

Recent Advances in Real Algebraic Geometry and Quadratic Forms

by Bill Jacob

Author	: Bill Jacob
Publisher	: American Mathematical Soc.
Total Pages	: 416
Release	: 1994
Genre	: Mathematics
ISBN	: 0821851543

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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.

Semidefinite Optimization and Convex Algebraic Geometry

by Grigoriy Blekherman

Author	: Grigoriy Blekherman
Publisher	: SIAM
Total Pages	: 487
Release	: 2013-03-21
Genre	: Mathematics
ISBN	: 1611972280

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

Probability on Algebraic Structures

by Gregory Budzban

Author	: Gregory Budzban
Publisher	: American Mathematical Soc.
Total Pages	: 250
Release	: 2000
Genre	: Mathematics
ISBN	: 0821820273

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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.