Logical Approaches to Computational Barriers

Domain theory and the causal structure of space-time

Speaker:
| Prakash Panangaden |

Author(s): |
Keye Martin and Prakash Panangaden |

Domain theory was developed by Dana Scott, Gordon Plotkin, Mike Smyth and others as a tool for understanding recursive programs and reflexive types in computation. Mathematically it is a theory of topological order structures: the order captures the notion of approximation while the topology captures the notion of limit. There is an intimate tie-up between the order and the topology which was explored by Scott, Lawson, Keimel and many others. This continues to be an active area of research especially in the context of probabilistic computation. In general relativity the causal structure of space time is also modelled by a partial order. Surprisingly, the mathematics of domain theory fits in a very pleasing manner with the theory of causal structure. Keye Martin and I were able to show how to reconstruct the topology of space-time from the causal order alone. Furthermore, we were able to show the existence of natural domain theoretic structures leading to a notion of "approximate points" in space-time. In this talk I will give an overview of these results.

websites: Arnold Beckmann | 2007-11-18 |