Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known a

A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.

What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? H

Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Non