Matrix reduction approaches to interpolation problems: a review withremarks
Rick Miranda
(Colorado State University)

About ten years ago M Dumnicki developed some techniques for interpolation problems related to a careful study of the rank of the matrices involved. Using these techniques he was able to extend the state of the art at the time, bringing certain problems into the range of computer analyses; this enabled him to prove that linear systems in the plane satisfied the SGHH conjecture for homogeneous multiplicities up to 42, the record then. We'll review the method, and consider some refinements, and applications to systems with ten points. The talk should be accessible to non-experts.