of utilizing flat norm computations for higher dimensional data. Similar to the flat norm-based signatures for distinguishing shapes in two dimensions [45], could we define shape signatures using multiscale simplicial flat norm computations to characterize the geometry of sets in arbitrary dimensions? The sequence of optimal multiscale simplicial flat norm decompositions of a given set for varying values of the scale parameter λ captures all the scale information of its geometry. Could we represent all this information in a compact manner, for instance, in the form of a barcode? We acknowledge the financial support from the National Science Foundation (NSF) through grants DMS-0914809 and CCF-1064600. Acknowledgments 50