Cosmological simulations of structure formation and the Vlasov equation

In cosmology numerical simulations of structure formation are now of central importance, as they are the sole instrument for providing detailed predictions of current cosmological models for a whole class of important constraining observations. These simulations are essentially molecular dynamics simulations of N (>> 1), now up to of order several billion) particles interacting through their self-gravity. While their aim is to produce the Vlasov limit, which describes the underlying (``cold dark matter'') models, the degree to which they actually do produce this limit is currently understood, at best, only very qualitatively, and there is an acknowledged need for ``a theory of discreteness errors''. In this talk I will describe, for non-cosmologists, both the simulations and the underlying theoretical models, and will then focus on the issue of discreteness, describing some recent progress in addressing this question quantitatively.