The Farey framework for SL2-tilings
This website is devoted to the project on using a combinatorial approach to explore the connections between number theory and geometry that arise around Conway–Coxeter friezes and SL2-tilings over integer numbers and other rings, carried out at the Open University, UK.
August 2024 highlights
- Triangulations and friezes, an interactive demonstration of the connections between triangulated polygons, paths in the Farey graph, Conway–Coxeter friezes, and cluster variables in the cluster algebra of type An.
- Working within our group during his summer internship, Sammy Benzaira obtained some results on the enumeration of friezes over ℤ/nℤ. A short paper coming soon.
Gallery
Two paths in the Farey graph in the Poincaré disk, corresponding to a certain SL₂-tiling
Portions of the Farey graph (grey), Ford circles (blue), and the truncated Farey graph (black) in the upper half-plane
Farey surface of a certain wild SL₂-tiling
The Farey complexes over integers modulo 5, 6, 7: icosahedron, hexagonal torus, Klein quartic
The project is funded by EPSRC grants EP/W002817/1 and EP/W524098/1.
SL2-tilings