You are probably familiar with a number of integer sequences determined by recurrence relations, such as the arithmetic sequences, the geometric sequences, the Fibonacci sequence, and so on. In this lecture, I will introduce a kind of integer sequences called the friezes, which are determined by curious recurrence relations. The friezes enjoy a number of remarkable properties that one might not expect from their definition. The most basic friezes were discovered by Conway and Coxeter in the 1970s. The more general friezes are defined from directed graphs and hide a universal mathematical structure called cluster algebras, discovered by Fomin and Zelevinsky earlier this century. I will present them as time permits.

NOTE:
- This lecture was conducted only in Japanese.