The Penrose tiling in fundamental physics
I will begin by introducing the Penrose tiling — the most famous example of a self-similar quasiperiodic pattern. In addition to its beauty and mathematical interest, this pattern already has one famous physical application, as a model for novel materials (quasicrystals) discovered in the 1980s. But in recent years this tiling (and its cousins) have also made a number of other striking appearances in quite different areas of theoretical physics: they turn out to be blueprints for quantum error correcting codes; and to also arise naturally in attempts to discretize the so-called “holographic” or “gauge/gravity” formulation of quantum gravity. I will give an introduction to these topics, and their connections to one another.