Frieze patterns are infinite strips of numbers satisfying certain determinantal identities. Originally motivated by Gauss’ “miraculous pentagram” identities, these patterns have since been connected to triangulations, integrable systems, representation theory, and cluster algebras. In this talk, we will review a few characterizations and constructions of frieze patterns, as well as a generalization which allows friezes with a “ragged edge” described by a juggling function. These “juggler’s friezes” correspond to special points in positroid varieties, in direct analogy with how classical friezes correspond to special points in Grassmannians.
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