Simulating hyperbolic space on a circuit board

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Synopsis

Looking for new bathroom tiles? Why don't you try regular 7-gons this time! Only requirement: You'd need to live in hyperbolic space of constant negative curvature. To see how this would be like, such tilings have been realized in recent breakthrough experiments in circuit quantum electrodynamics and electrical circuits, where particles are tricked into believing that space is hyperbolic. After an elementary introduction to hyperbolic geometry, I will discuss the intriguing crystallographic properties of hyperbolic lattices and exemplify hyperbolic matter on the fascinating example of hyperbolic graphene.