Thursday, July 13, 2023 - 17:15 in V2-210/216
Deformations and dynamics of the Hat family of tilings
A talk in the Mathematisches Kolloquium & Mathematisches Kolloquium (SFB 1283) series by
Lorenzo Sadun from University of Texas, Austin
| Abstract: |
Shape deformations of a tiling are governed by its first Cech
cohomology. For the Hat, a simple computation shows that there is a
4-parameter family of tiling spaces, topologically conjugate but not MLD
to the original. This includes the 1-parameter family developed by Smith
et al, a self-similar CAP tiling, and Socolar's golden Key tiling. The
spectrum of all of these tilings is pure point and equals
$\mathbb{Z}[\xi, \phi]$, where $\xi = \exp(2 \pi i/6)$ and $\phi$ is the
golden mean. All tilings are cut-and-project as well as hierarchical,
with the exact same total space and window, only with different
projections to physical space. Similar comments apply to the recently
discovered Spectre tilings. This is joint work with Michael Baake and
Franz Gaehler.
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