Programme Speaker: Dr. David Rideout Title: Spatial Hypersurfaces in Causal Set Cosmology Abstract: Within the causal set approach to quantum gravity, a discrete analog of a spacelike region is a set of unrelated elements, or an ``antichain''. In the continuum approximation of the theory, a moment-of-time hypersurface is well represented by an ``inextendible'' antichain. We construct a richer structure corresponding to a ``thickening'' of this antichain containing non-trivial geometric and topological information. We find that covariant observables can be associated with such thickened antichains and transitions between them, in classical stochastic growth models of causal sets. This construction highlights the difference between the covariant measure on causal set cosmology and the standard sum-over-histories approach. The resulting re-phrasing of the sum-over-histories may be fruitful in other approaches to quantum gravity. Talk: Transparencies, Recorded Talk