Speaker: Richard Kenyon (Yale University)
Title: The multitiling model
Abstract: The study of random tilings is a cornerstone area of combinatorics and probability. Unfortunately the tiling problem is NP-hard even in quite simple-looking cases. We study a tractable variant, the multitiling model, where we tile a region with high multiplicity. In the limit of large multiplicities we compute the asymptotic growth rate of the number of multitilings: the free energy of the multitiling model. We show that the individual tile densities tend to a Gaussian field with respect to an associated discrete Laplacian. For tilings with translates of a polyomino on Z^2 we find crystallization phenomena (and accompanying phase transitions), and even naturally occurring quasicrystals.
This is joint work with Andrei Pohoata (Yale).