Colored Links and Topological Vortex Structures

Topological vortices are intriguing defects that emerge in a wide range of physical systems, including Bose–Einstein condensates and liquid crystals. In this talk, I will describe how the global structure of such vortices can be captured pictorially using colored link diagrams—or more generally, colored embedded graphs. Through a variety of examples, I will illustrate how this framework can be used to classify and analyze vortex configurations. In particular, I will highlight conditions under which these structures are topologically protected, in the sense that they cannot decay into collections of disjoint loops without destroying the underlying phase of the system. These investigations naturally give rise to new topological invariants of colored links, which can be used to distinguish and classify such vortex structures.