Suppose we have a region that is a bounded subset of the square grid (such as a finite union of squares on an infinite chessboard). Consider the problem of tiling this region with 1x2 and 2x1 dominoes. There are several questions that arise:
– How can we tell whether such a region is tileable in the first place?
– If such a region is tileable, then how many tilings exist?
– What does a "typical" tiling look like?
In this talk, we will introduce several theorems that answer these questions, and explore basic examples that illustrate these results. We will also see how tilings of large Aztec diamonds can create some interesting surfaces!