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Aperiodic tilings and quasicrystals

The aim is to understand the relationship between substitution and
projection properties of aperiodic tilings such as the Penrose tiling.
The following issues are of interest
- Classification of substitution rules for classes tilings with
special projection properties. (In the Penrose case: substitution rules
for canonical projection tilings)
- Understanding the relationship between the set of substitution rules
(often a countable infinity) for substitution tilings.
- Generalized continued fractions and tilings.
- Substitution tilings with non-uniform scaling.

Work in progress with Edmund Harriss (Queen Mary).
For an impression of the topic, see Andrew Lewis's short
introduction , inspired by a 3rd year course I taught at Warwick in
1998 and 1999.