Crystallography of Hyperbolic Lattices

Hyperbolic lattices are tessellations of the hyperbolic plane using, for instance, heptagons or octagons. They are relevant for quantum error correcting codes and experimental simulations of curved space quantum physics in circuit quantum electrodynamics. Underneath their perplexing beauty lies a hidden and, perhaps, unexpected periodicity that allows us to identify the unit cell and Bravais lattice for a given hyperbolic lattice. This paves the way for applying powerful concepts from solid state physics and, potentially, finding a generalization of Bloch's theorem to hyperbolic lattices. In my talk, I will explain how to build a hyperbolic crystallography and apply it to physically relevant problems.