By Ian Short
Appears in collection : Frieze patterns in algebra, combinatorics and geometry / Frises en algèbre, combinatoire et géométrie
This short course is about modelling SL2-tilings and Coxeter frieze patterns with Farey complexes. The first talk concerns tame frieze patterns over the integers. We introduce the Farey tessellation of the hyperbolic plane, drawing inspiration from the theory of dessins d'enfants. The geometric and numeric properties of the Farey tessellation shed light on known results on classifying frieze patterns and they provide a framework for new results. This approach originated in work of Morier-Genoud, Ovsienko, and Tabachnikov; we will discuss their ideas and generalisations. There will be diagrams aplenty, several exercises, and a few open questions.
By Valentin Ovsienko
By Alain Connes
