Paul Smith (Cambridge)

Bootstrap percolation is a broad class of monotone cellular automata, which has links to the Glauber dynamics of the Ising model and other areas of statistical physics. Starting with random initial conditions, the question is to determine the threshold for complete occupation of the underlying graph. Until relatively recently, only nearest-neighbour models (and relatively minor variants of these models) had been studied -- and these are now very well understood. In this talk I will discuss a new `universality' theory for bootstrap percolation, which has emerged in the last few years. In particular, I will explain a classification of two-dimensional models, give more precise results for so-called `critical' models (also in two dimensions), and talk about a new classification theorem for higher dimensional models.