Title: Non-equilibrium Dynamics of Kinetically Constrained Models

Abstract: Kinetically constrained models (KCMs) are spin systems on integer lattices, where each vertex can be labeled either 0 or 1, which evolve according to a very simple rule: i) with rate one and independently for each vertex, a new value 1/0 is proposed with probability 1-q and q respectively; ii) the proposed value is accepted if and only if the neighbouring spins satisfy a certain constraint. Despite of their apparent simplicity, these models have attracted much attention both in the mathematics and physics communities. The out of equilibrium dynamics are extremely rich and display many of the key features of the dynamics of real glasses, such as; an ergodicity breaking transition at some critical value, huge relaxation times close to the critical point, dynamic heterogeneity (non-trivial spatio-temporal fluctuations of the local relaxation to equilibrium) and ageing just to mention a few. We will review some of the recent advances in the understanding of the rich dynamics of these models as they relax toward equilibrium.