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A domino tiling is a covering of a region on the plane using dominoes without gaps or overlaps. I will begin by discussing its background from physics, called the dimer covering, which models how diatomic molecules stick on a crystal surface. This talk focuses on two aspects of domino tilings: in combinatorics, I will review their symmetry classes on the Aztec diamond and present new properties; in algebra, I will establish a connection between specific tiling models and symmetric functions from the viewpoint of Macdonald theory. Finally, I will introduce my recent research in dynamical combinatorics, a vibrant field at the intersection of discrete dynamical systems and combinatorics. This talk does not assume any prior background.

More information: https://sites.google.com/view/yllee/