James Propp

Abstract:   Certain lattice models, introduced by chemists and physicists in the study of homogeneous bulk matter, turn out to be interesting toy models of non-homogeneous matter as well. These lattice models can be most readily defined via tilings of finite plane regions.

In this talk I will focus largely on tilings by dominoes, and give a quick tour of results discovered in the past ten years (some of it obtained by, or with the assistance of, undergraduates at colleges in the Boston area). The most recent of these results shows how the calculus of variations can be used to predict what will happen in the interior of a random tiling, in terms of what behavior has been prescribed along the boundary. No background in statistical mechanics or the calculus of variations will be assumed.