Doktorandseminarium: Quasicrystals and densities
- Plats: Ångströmlaboratoriet 4005
- Föreläsare: Gustav Hammarhjelm
- Kontaktperson: Volodymyr Mazorchuk
After a brief account of the discovery of physical quasicrystals, I will give examples of mathematical quasicrystals, the main one will be the Ammann-Beenker point set, obtained as the vertices of a substitution tiling. Another method of constructing quasicrystals, namely the Cut-and-project construction, will also be shown.
The (asymptotic) density of a point set will be defined. We will see that the density of visible points of the integer lattice equals the probability that two random integers are relatively prime. This density will be calculated and identified as a very familiar constant. Finally, I hope to be able to describe how the density of visible points of the Ammann-Beenker point set can be obtained through a similar calculation.