Frieze patterns and Farey complexes | Vidéo | Carmin.tv

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Frieze patterns and Farey complexes

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.

Information about the video

Date of recording 12/05/2025
Date of publication 04/06/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20346603
Cite this video Short, Ian (12/05/2025). Frieze patterns and Farey complexes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20346603
URL https://dx.doi.org/10.24350/CIRM.V.20346603

Domain(s)

Bibliography

SHORT, Ian. Classifying SL₂-tilings. Transactions of the American Mathematical Society, 2023, vol. 376, no 01, p. 1-38. - https://doi.org/10.1090/tran/8296
SHORT, Ian, VAN SON, Matty, et ZABOLOTSKII, Andrei. Frieze patterns and Farey complexes. arXiv e-prints, 2023, p. arXiv: 2312.12953. - https://doi.org/10.48550/arXiv.2312.12953

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