This project is an equipment grant under the activity Grants For Scientific Computing Research Equipment For The Mathematical Sciences program. The project involves the purchase of special purpose equipment dedicated to the support of research in the mathematical sciences. In general, this equipment is required jointly by several research projects and would be difficult to justify on one project alone. This research equipment support from the National Science Foundation is coupled with discounts and contributions of equipment from manufacturers and significant cost-sharing from the submitting institution. This project provides a good example of university, industrial, and government cooperation in the support of basic research in the mathematical sciences. This equipment will be utilized to support the following research: (1) MACSYMA, MACAULY, BMDP, and SPSSx will be used to study the relationship between numerical invariants of rational plane curves, (2) parameter spaces of complex dimensional families of invariant quadratic differentials will be examined graphically, (3) Julia sets of entire and meromorphic functions and stable sets of Kleinian groups will be examined, and (4) the connection between measures and recurrence coefficients involving orthogonal polynomials will be studied. The projects involve high speed multiple precision arithmetic, large memory requirements, and artificial intelligence.
