The Department of Mathematics at Oklahoma State University will purchase and maintain a computational server dedicated to the support of research in the mathematical sciences. The equipment will be used to carry out symbolic algebra computations by our research faculty; including, in particular,
1. "Intersection theory computations on moduli spaces of curves", (C. Faber). Computations aimed at verifying a detailed conjectural description of the tautological ring of the moduli space of smooth curves of genus greater than or equal to 2; and an extension of the algorithm for intersecting divisors on the compactification this moduli space to an algorithm that will compute intersection numbers of arbitrary classes in the tautological rings of the compactified moduli space.
"SCHUBERT: a MAPLE package for intersection theory in algebraic geometry", (S. Katz). Continuation of the development with Stromme of a symbolic algebra package for research in intersection theory in algebraic geometry.
3. "SHEAFHOM, and Hecke operators on the cuspidal cohomology of arithmetic groups", (M. McConnell). Further development of the programs SHEAFHOM that allow one to work with sheaves, spectral sequences, and intersection homology; and calculations aimed at identifying the cuspidal cohomology of certain congruence subgroups of GL(4,Z) and computing the Hecke operators on it.
4. "Computing Projects in Numerical Analysis and Approximation Theory", (H.G.W. Burchard). Data fitting by means of primal-dual interior points methods.
