Spacetime Quasicrystals or: How I Learned to Stop Worrying and Love the Rhomb

Spacetime Quasicrystals or: How I Learned to Stop Worrying and Love the Rhomb Non-repeating tilings of Euclidean space (e.g. the famous Penrose tiling) are of interest in physics, and are mathematically well-understood. In spaces with a time direction, however, discrete geometry as a whole becomes distinctly harder to formulate. This talk will introduce the algebraic machinery behind Penrose-like patterns in Euclidean space, then show what happens when we try to pull the same tricks in spacetime, and have a go at constructing spacetime quasicrystals. If time allows, we might even be able to fit in a tiny bit of algebraic number theory!