Topological defects in soft matter

Topology plays a crucial role in many branches of physics. One of the exciting and versatile systems for studying topological structure of matter are nematic liquid crystals and their colloidal composites, where singularities in nematic order parameter emerge as topological defects. Under constraints imposed by boundary conditions and different topologies of inserted colloids, distinct defects are formed, such as disclination lines, knots, links and particle-induced defect loops. We explore the structures of fields and defects, study their topological properties and how to manipulate them.