"Geometry and Polynomial Systems - Theory and Application" Peter F. Stiller stiller@alggeo.math.tamu.edu Dr. Peter F. Stiller Professor of Mathematics and Computer Science and Assistant Director of the Institute for Scientific Computation Texas A&M University College Station, TX 77843-3368 USA stiller@alggeo.math.tamu.edu We discuss some general geometric aspects of polynomial systems and their solution by computer algebra systems. This includes a discussion of certain anomalies that can be introduced when solving certain systems. If time permits, we will also discuss some applications of computer algebra to solving systems that arise in dexterous manipulation planning problems in robotics and in the problem of indexing geometric databases for content-based retrieval (for example image databases.) In the first case, the polynomial systems characterize the so-called contact formation cells of a manipulator system. These are constraint varieties in configuration space that reflect a particular type of grasp. In the second case, we are concerned with generating the equations that define the correspondence (in the sense of algebraic geometry) between the geometric invariants of certain features of a set of objects and the invariants of the images of those features.