Abstract:

How many ways are there to tile an n x n chessboard with unmarked dominoes? This question dates back to the early 20th century, when physicists used domino tilings as a statistical mechanical model of diatomic molecules. For some regions (that are natural like the chessboard), we can exactly count the number of tilings with simple formulae, while for other regions we can count using efficient algorithms. We will survey some of these methods and will show algorithms for generating random domino tilings. As we shall see, random tilings reveal a rich underlying structure that has led to deep and beautiful mathematical discoveries.

This lecture is aimed at an undergraduate audience.