The dimer model on the hexagonal lattice

The dimer model is the study of random perfect matchings on graphs, and has a long history in statistical mechanics. On the hexagonal lattice it is equivalent to tilings of the plane by lozenges and to 3D stepped surfaces called skew plane partitions - 3 dimensional analogues of Young diagrams with a partition removed from the corner. This particular instance of the model has been intensely studied in the past 15 years by Borodin, Kenyon, Okounkov, Reshetikhin and many co-authors. I will discuss the scaling limit of the model under a certain family of measures called "volume"-measures, the phase-transition phenomenon in this model, the effects of varying the boundary conditions on the limit shape, the nature of local fluctuations in various regions of the limit shape and connections with random matrix theory.