Friezes, Geometry seminar talk by Andrei Zabolotskii

Friezes, originally introduced by Coxeter, are simple objects which however turned out to be connected with surprisingly many seemingly unrelated concepts from a variety of subjects. These include combinatorics (polygon dissections), number theory (continued fractions), geometry (the Farey graph), and algebra (cluster algebras — a hot topic of their own). I will survey these connections using interactive visualisations, introduce the family of basic examples of cluster algebras, and present a new connection between not-necessarily-positive friezes and cluster algebras.