The topology of defects
Codimension two (or higher) defects arise in many pattern forming systems, often coexisting with codimension one defects (domain walls). These codimension two defects usually carry a topological "charge" which strongly constrains their dynamics.
I will talk about point defects in various 2D systems (convection patterns, liquid crystals, and thin hyperbolic elastic sheets). I then discuss the nontrivial ways in which the underlying topology of these defects governs their birth, dynamics, stability, and their role in applications.