Chiral liquid crystals seen through the lens of contact topology

Date: Thursday 14 March 2024

Abstract

Liquid crystals are a phase of matter in which the material is soft and flows like a liquid, but the molecules also retain long-range orientational order like a crystal. They have many applications in display technology, phontonics, sensors, and colloidal assembly. In addition to these applications liquid crystals also provide beautiful realisations of results and structures from the field of topology, and topological methods have been fundamental in developing our understanding of these materials. Recently interest has grown in liquid crystals formed from materials with molecular chirality, which have an even greater scope for applications and may also be useful as models for epithelial tissues and membranes.

I will overview the homotopy theory perspective on liquid crystals and their defects, and the ways in which the predictions of this theory have been realised in experiments. I will then present a new mathematical theory of chiral liquid crystals based on ideas from contact topology and singularity theory. I use this theory to classify the defects of chiral materials and show how this classification explains structures found in recent experiments, as well as how it offers a new perspective on defects in achiral materials.