Topological quantum field theories and Markovian random fields
Résumé
We discuss an analogy between topological quantum field theories and the theory of Markov processes, which both rely on the combination of a notion of transition and a notion of locality. We assume no prior knowledge of topological quantum field theory (TQFT) and devote the first section to a motivation of its definition, which was originally given by M. Atiyah. We then discuss 1- and 2-dimensional TQFT's, and a mild generalization of them which incorporates a notion of time and is suited to the parallel with Markov processes.
This text is a written version of a talk whose emphasis was on explaining and illustrating ideas. There are few rigorous statements in it, and no proof.