Fix a ring R, a graph G, and a map E from the edges of G to the ideals of R. An algebraic spline on the pair (G,E) is a vertex labeling of G so that if two vertices are connected by an edge, their labels differ by an element of the corresponding ideal.  Algebraic splines are interesting objects unto themselves, but by choosing G and E appropriately, the pair (G,E) becomes a GKM graph (Goresky-Kottwitz-MacPherson) for a particular algebraic variety, such as flag variety or Grassmannian. The splines on these particular graphs are isomorphic to the equivariant cohomology rings of their algebraic varieties. Furthermore, projections of these splines give equivariant cohomology rings for particular spaces that are not GKM spaces, but are contained in GKM spaces.  In this talk we will discuss the Peterson variety in particular.