Abstract
Topology, and in particular the concept of topological defects, plays a central role in the physics of crystalline materials. These defects are key to understanding two-dimensional melting, as well as the emergence of plasticity and mechanical failure. However, identifying disorder typically relies on having a well-defined reference ordered state for comparison. For this reason, in amorphous solids, which lack long-range translational order, the notion of topological defects has historically been considered ill-defined and of limited use. As a consequence, fundamental questions such as the origin of plasticity in glasses have remained unresolved. In this talk, building on recent developments, I challenge this prevailing view. I will argue that topological defects can, in fact, be meaningfully defined in disordered solids, and may play a role just as fundamental in their physics as they do in crystals. I will present theoretical arguments, numerical simulations, and experimental results that support this perspective, and conclude by outlining promising directions for future research.