Contemporary Mathematics 2000; 287 pp; softcover Volume: 253 ISBN10: 0821808044 ISBN13: 9780821808047 List Price: US$87 Member Price: US$69.60 Order Code: CONM/253
 This volume contains 16 carefully refereed articles by participants in the Special Session on Real Algebraic Geometry and Ordered Algebraic Structures at the Sectional Meeting of the AMS in Baton Rouge, April 1996, and the associated Special Semester in the spring of 1996 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. 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 latticeordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higherlevel) 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 structurestwo subjects that are obviously related, but seldom brought together. Readership Graduate students and research mathematicians interested in algebraic geometry. Table of Contents  M. E. Alonso and M. P. Vélez  On real involutions and ramification of real valuations
 E. Becker, V. Powers, and T. Wörmann  Deciding positivity of real polynomials
 J.P. Brasselet  Radial vector fields and the PoincaréHopf theorem
 S. Finashin  A generalization of the ArnoldViro inequalities for real singular algebraic curves
 P. M. Gilmer  Floppy curves, with applications to real algebraic curves
 D. Gondard and M. Marshall  Towards an abstract description of the space of real places
 L. GonzalezVega  A special quantifier elimination algorithm for Pham systems
 M. Henriksen and F. A. Smith  A look at biseparating maps from an algebraic point of view
 J. Huisman  Real Teichmüller spaces and moduli of real algebraic curves
 J. Huisman  Correction to "A real algebraic vector bundle is strongly algebraic whenever its total space is affine"
 F.V. Kuhlmann and S. Kuhlmann  The exponential rank of nonarchimedean exponential fields
 L. Noirel and D. Trotman  Subanalytic and semialgebraic realisations of abstract stratified sets
 J. Ohm  On the vector space defect for valued field extensions
 G. M. Polotovskii  On the classification of decomposable 7th degree curves
 M. J. de la Puente  The complex spectrum of a ring
 B. Reznick  Some concrete aspects of Hilbert's 17th problem
 M. Shiota  Semialgebraic singularity theory
