Topological defects such as cosmic strings or domain walls may have formed during a symmetry breaking phase transition in the early universe.  After formation, defects evolve into a scaling network whose dynamics is governed by the Nambu-Goto action, which typically predicts the formation of cusps, namely, events in which defects self-intersect and where a great amount of energy is concentrated. In this talk I will present how the formation of cusps can be understood in terms of the mathematical catastrophe theory, and study the possibility of (primordial) black hole formation from such events in cosmologically viable scenarios..

https://indico.math.cnrs.fr/event/16023/