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Textures and Topology in Liquid Crystals

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The Mathematics of Liquid Crystals

The textures of liquid crystals have always been central in identifying mesophases and understanding their properties. They are deeply connected with topology, both of the liquid crystal and of the environment that it lives in, so that controlling and describing topological properties provides a key tool in constructing and understanding complex three-dimensional textures. I will describe two applications of topological ideas to studying mesophases: the general characterisation of three-dimensional textures in nematics—illustrated through the analysis of torons and the Hopf fibration in confined cholesterics—and the formation of elegant knots and links around colloidal particles representing non-orientable surfaces.

This talk is part of the Isaac Newton Institute Seminar Series series.

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