Topology of nematic liquid crystal colloids confined to two dimensions

We present a brief overview of recent development in the field of nematic colloids with an emphasis on the topology of colloidal structures and recently discovered topologically nontrivial defect configurations. Nematic colloids are complex soft-matter systems, in which the topology of defects, induced by colloidal inclusions, can be controlled and varied locally by laser tweezers and other external fields. We discuss the role of elasticity driven colloidal interactions and demonstrate the importance of precise optical manipulation of topological defects for a targeted design of entangled structures. We conclude that the interplay between particle and defect topologies in liquid crystals provides an exciting journey to the burgeoning area of applied topology and opens several new directions in advanced engineering of soft materials.