Latham Boyle | The Penrose tiling, self-similar quasicrystals, and physics

Speaker: Latham Boyle (Perimeter Institute)
Date: October 27, 2022

Title: The Penrose tiling, self-similar quasicrystals, and physics
Abstract: 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 already has one famous physical application, as a model for novel materials called quasicrystals, discovered in the 1980s. But, as I will explain, such patterns also naturally crop up in other quite different physical situations, where scale invariance plays an important role. I will introduce some examples that I find fascinating. One comes from recent efforts to formulate a "discrete" version of the "AdS/CFT" or "gauge/gravity" correspondence, by replacing the negatively curved (hyperbolic) "bulk" space by a regular tiling of hyperbolic space. I will do my best to explain these ideas with pictures, and in a way that I hope will be of interest to both physicists and mathematicians.