An introduction to the mathematical description and computational enumeration of periodic tilings and nets.

13^th May 2019, 11:00 Ground floor boardroom, MIF
Vanessa Robins
ANU, Applied Maths

Abstract

Periodic tilings and nets are simplified models of atomic arrangements in crystals. Systematic methods for describing and enumerating possible crystal structures are based on factoring out either the translational periodicity or the full crystallographic symmetry. The mathematical version of “factoring out” gives us an object called an orbifold. I will explain how orbifolds encapsulate the essential elements of a crystallographic group and provide an effective basis for the enumeration of hypothetical crystalline structures. The presentation will be informal and largely based on pictures and examples, hopefully accessible to non-specialists.