Includes bibliographical references.

Equations of parametric curves and surfaces via syzygies ; An explicit description for the triangular decomposition of a zerodimensional ideal through trace computations ; Numerical irreducible decomposition using projections from points on the components ; Counting stable solutions of sparse polynomial systems in chemistry ; Central configurations in the Newtonian ody problem of celestial mechanics ; A power function approach to Kouchnirenko's conjecture ; Finiteness for arithmetic fewnomial systems ; Constructing doubleexponential number of vectors of multiplicities of solutions of polynomial systems ; Computing sparse projection operators ; Grobner bases of abelian matrix groups ; Lexicographic Grobner bases of 3dimensional transportation problems ; Simplicial complexes and syzygies of lattice ideals ; Algorithmic determination of the rational cohomology of complex varieties via differential forms ; Differential algebras on semigroup algebras ; Noncommutative Grobner bases and Hochschild cohomology David A Cox ; Gema M DiazToca and Laureano GonzalezVega ; Andrew J Sommese Jan Verschelde and Charles W Wampler ; Karin Gatermann ; Ilias S Kotsireas ; Domenico Napoletani ; J Maurice Rojas ; Dima Grigoriev ; Carlos D'Andrea and Ioannis Z Emiris ; Bernd Sturmfels ; Giandomenico Boffi and Fabio Rossi ; E Briales A Campillo P Pison and A Vigneron ; Uli Walther ; Mutsumi Saito and William N Traves ; Michael J Bardzell