Application of a Numerical Version of Terr Acini's Lemma for Secants and Joins.- On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces.- Intersections of Schubert varieties and other permutation array schemes.- Efficient Inversion of Rational Maps Over Finite Fields.- Higher-Order Deflation for Polynomial Systems With Isolated Singular Solutions.- Polars of Real Singular Plane Curves.- Semidefinite Representation of the k-Ellipse.- Solving Polynomial Systems Equation by Equation.

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 2006 is one tangible indication of the interest. This volume of articles captures some of the spirit of the IMA workshop.