Topological quantum field theories and Markovian random fields

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 TQFTʼs, 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.