Topological order: umbilics in chiral liquid crystals

Workshop on Topology: Identifying Order in Complex Systems
Topic:Topological order: umbilics in chiral liquid crystals
Speaker:Gareth Alexander
Affiliation:University of Warwick
Date:Saturday, October 18
Time/Room:9:30am - 10:30am/Hill Center 705, Rutgers University

Recent experimental advances have opened the door to laboratory realisations of a large range of complex textures with distinctive topological properties, including knots, skyrmions and “Hopf fibrations” in optics, fluids, helical magnets and liquid crystals. We will show how the order in these materials can be described in terms of certain naturally defined vector bundles, whose generic zeros we dub umbilics and which manifest themselves in magnetic skyrmions and the lambda defects of cholesteric liquid crystals. Focussing on the examples from liquid crystals we will explain how the geometry of these vector bundles captures the geometry of the material, while their characteristic classes convey the topology.