PIMS- UAlberta Statistics Colloquium: Latham Boyle

I will begin by introducing the Penrose tiling -- the most famous example of a self-similar quasi-periodic pattern. In addition to its beauty and mathematical interest, this pattern has a famous physical application to exotic materials called quasicrystals. In this talk, I will also discuss two new physical contexts in which such patterns appear:

(1) First, I will explain how a regular tiling of negatively-curved (hyperbolic) space naturally decomposes into a sequence of self-similar quasicrystalline slices, with each slice related to its neighbors by an invertible local substitution rule. (In particular, the self-dual tiling of hyperbolic space by icosahedra decomposes into a sequence of Penrose-like tilings, as originally conjectured by Thurston.) This relates to recent efforts to formulate discrete versions of the holographic principle.

(2) Second, I will introduce the lattice II_{9,1} (the even self-dual lattice in 9+1 dimensional Minkowski space), and the 3+1 dimensional quasicrystals living inside it, and explain why they are interesting from both a mathematical and physical standpoint.