Lecture on topological crystallography

T. Sunada

Abstract: This is an expository article on modern crystallography based on discrete geometric analysis, a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability, which has been developed in the last decade. The mathematical part relying on algebraic topology is fairly elementary, but may be still worthwhile for crystallographers who want to learn how well-established mathematics is effectively used in the practical science. A brief history of crystallography is also explained.