Periodic driving has recently emerged as an extremely versatile tool to engineer and tune exotic topological states of matter in a controlled way. For example, periodic driving generates a cascade of Majorana edge modes beyond the static limitation of one per edge in the Kitaev chain, resulting in a hierarchy of associated topological phase transitions (TPT's). Understanding the critical behavior of such out-of-equilibrium TPT's is therefore an important step in the quest to harness the unique properties of Floquet systems.

In this talk, I will compare the nature of the topological phase transitions in various static and periodically driven systems by means of a renormalization group procedure on the curvature functions used to construct topological invariants. I will demonstrate how this very transparent and powerful method can identify the topological phase boundaries and assess the nature of their criticality in terms of universality classes. This procedure works even for topological phases hosting anomalous edge modes, i.e. phases where the Floquet band Chern number does not correspond to the number of edge states.