36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"Local rules for Cut and Project Tilings"

Fernique, Thomas

The cut-and-project method is a classical method to define quasi-periodic tilings, which are often used to model quasicrystals. Penrose or Ammann-Beenker tilings are well known examples. A possible stabilization of quasicrystals in terms of short-range energetic interactions leads to the question of which tilings are characterized by their local patterns only. This is for instance the case for Penrose tilings, but not for Ammann-Beenker tilings. We propose an overview of the main results known to date.

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