Contains 15 papers from the November 1999 meeting, beginning with a survey of the history of the problem by Yuri Matiyasevich (Steklov Institute of Mathematics, St. Petersburg). Topics include Hilbert's tenth problem for various rings and fields; local-global principles; the relation between Hilbert's tenth problem and conjectures in arithmetic geometry relating to the structure of the set of rational points on a variety via elliptic curves; Mazur's conjecture and Bnchi's problem; and Maurice Rojas' (City University Hong Kong) summary of his Ghent lectures concerning complexity results for computing with algebraic sets. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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