3 papers
math.PR2025
Emergence in graphs with near-extreme constraints
Charles Radin, Lorenzo Sadun
We consider entropy-optimal graphons associated with extreme and near-extreme constraints on the densities of edges and triangles. We prove that the optimizers for near-extreme con…
math.DS2025
Dynamics and topology of the Hat family of tilings
Michael Baake, Franz Gähler, Lorenzo Sadun
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous…
math.DS2024
How big is a tiling's return module?
Abigail Perryman, Lorenzo Sadun
The rank of a tiling's return module depends on the geometry of its tiles and is not a topological invariant. However, the rank of the first \v Cech cohomology giv…