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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.
Table of Contents
Semialgebraic topology in the last ten years.- Algebraic geometric methods in real algebraic geometry.- On the classification of decomposing plane algebraic curves.- Real algebra and its applications to geometry in the last ten years: Some major developments and results.- Topology of real plane algebraic curves.- Moduli problems in real algebraic geometry.- Constructing strange real algebraic sets.- More on basic semialgebraic sets.- Mirror property for nonsingular mixed configurations of one line and k points in R3.- Families of semialgebraic sets and limits.- A hopf fixed point theorem for semi-algebraic maps.- On regular open semi-algebraic sets.- Sums of 2n-th powers meromorphic functions with compact zero set.- Pseudoorthogonality of powers of the coordinates of a holomorphic mapping in two variables with the constant Jacobian.- Trivialite's en famille.- Stiefel orientations on a real algebraic variety.- Subanaliticity and the second part of Hilbert's 16th problem.- The decidability of real algebraic sets by the index formula.- Proper polynomial maps: The real case.- Sur les ordres de niveau 2n et sur une extension du 17ème probleme de Hilbert.- Curves of degree 6 with one non-degenerate double point and groups of monodromy of non-singular curves.- The 17-th Hilbert problem for noncompact real analytic manifolds.- Construction of new M-curves of 9-th degree.- On linear differential operators related to the n-dimensional jacobian conjecture.- On a subanalytic stratification satisfying a Whitney property with exponent 1.- Une borne sur les degres pour le theoreme des zeros reel effectif.- Minimal generation of basic semi-algebraic sets over an arbitrary ordered field.- Configurations of at most 6 lines ofP 3.- Extensions of Rokhlin congruence for curves on surfaces.- Complexité de la construction des strates à multiplicité constante d'un ensemble algébrique den.- Real plane algebraic curves with many singularities.- Effective stratification of regular real algebraic varieties.