SPUR / RSI 2024 Lecture Series

Building 2, 2-449

Speaker : Scott SheffieldTitle : 3D domino tilingsAbstract :There are finitely many ways to cover a chessboard with 32 dominos (each domino covering two adjacent squares). What if one chooses one of these coverings uniformly at random? What does the typical domino tiling "look like"? There are various mathematical ways to ask and answer this question, and it turns out that the answers depend a lot on the shape of the region you are trying to tile. If one replaces the chessboard by another shape, the tilings typically "look" completely different. A lot of really powerful and beautiful mathematics has come from these seemingly simple questions.The 3D version of the problem is in some ways even more fun, and that is what I will talk about. This is based on recent joint work with Nishant Chandgotia and Catherine Wolfram. If you want to prepare a bit in advance, Catherine's slides are a great place to start: https://math.mit.edu/~wolframc/Penn-slides.pdf.Reception following lecture in breakout space 2-450!