The problem of tiling a given planar region is quite classical. A more modern approach is to consider the tilings of a given region under the light of statistical mechanics: given a measure on all possible tiling configurations of a large planar region, can we say how a ''typical'' tiling looks like? In this series of talks, we consider this problem when the region is the aztec diamond, and the tilings are dominos, distributed in a periodic fashion. It turns out that this model displays a quite rich, yet explicit, structure, and we plan to survey in details some recent developments in this model. Speaker(s): Yuchen Liao (University of Michigan)