Theory of 2D Lattice Invariants.

24^th March 2023, 14:00
Matthew Bright
MIF

Abstract

The central problem for our group is the representation of periodic structures as points in some continuous space, in the sense that a small perturbation of the structure itself gives rise to a small change in the position of the point which represents.
Our solution [1] to this problem for a simple periodic structure - the 2D Lattice - allows for many different kinds of representation, all topologically equivalent to a punctured sphere. The solution gives rise to a very natural quantification of the ‘asymmetry’ of a lattice - that is, the distance through which it would need to be distorted such that it became a lattice with a particular symmetry group. We will briefly recap the development of 2D Lattice Invariants and the associated chiral distances [2].
[1] V.Kurlin. Mathematics of 2D lattices. Foundations of Computational Mathematics.
[2] M.Bright et al. Geographic-style maps for 2D lattices. Acta Cryst A v.79 (2023), p.1-13.