Classifying crystal structures: geometric and arithmetic approach

  • Mario Nardone (Oxford University, Oxford, United Kingdom)
G3 10 (Lecture hall)


While the classification of cristals made up by just one atom per cell is well-known and understood (Bravais lattices), that for more complex structures is not. We present a geometric way classifying these crystals and an arithmetic one, the latter introduced in solid mechanics only recently. The two approaches are then compared. Our main result states that they are actually equivalent; this way a geometric interpretation of the arithmetic criterion in given.

Katja Bieling

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Stefan Müller

Max Planck Institute for Mathematics in the Sciences, Leipzig

Dominique Schryvers

University of Antwerp