Social aggregates are often modeled with networks, and network theory is therefore used to deduce properties of the aggregate from the topological properties of the associated network. However, in many real life cases, the nature of the aggregate does not lend itself to a network representation, because higher order connections may exist. As an example, think of a paper with three coauthors, say John, Mary, and Zach, versus three papers, each coauthored by two of the three scholars. In both cases we would think of John, Mary, and Zach connected to each other, but it is clear that the way in which the two situations must be modeled is quite different. In these situations (which arise in social contexts, as well as in authorship aggregates, for example), networks do not seem to offer the best model, and we are proposing the use of their higher dimensional counterparts, namely simplicial complexes. In this talk we offer the basic ideas behind our approach, and we discuss some ideas on centrality measures in this new context. In particular we will use the fact that simplicial complexes can be written as monomials to apply algebraic techniques to study the social aggregates modeled by simplicial complexes. The talk will present a number of directions for further research, and ideas for possible applications.