Abstract:  In a mass partition problem, we wish to split fairly a family of measures in R^d according to some geometric constraints.  For example, we may want to split R^d into two pieces using a single hyperplane, or into k convex pieces, and want each piece to have the same size in each given measure.  Given a way to split R^d, we are interested in the maximum number of measures we can always split fairly.  In this talk, we will describe how the use of topological properties of Stiefel manifolds allows us to prove old and new results in the area, simplifying significantly the technical machinery needed to solve these problems.