Title: Matroids and Regularity of Fat Points



Abstract: Given a scheme of fat points Z in P^n, the regularity index can be defined as the point where the Hilbert function of the quotient ring, R/I(Z), is equal to the degree. We discuss new results which give upper bounds on this regularity index, based on the linear position of the points in space. A key technique is some results in the theory of Matroid Partitions.