The theory of topological insulators and superconductors, developed over the last 3 decades, plays a central role in contemporary condensed-matter physics. These materials have an insulating bulk with topological invariants, and host "edge" states on their boundaries which give rise to universal, quantized surface conduction, even in the presence of onsite disorder (that would be expected to lead to their Anderson localization). The theory can also be applied to periodically driven systems, but its consequences here are less known. The PhD research of the applicant will aim to explore the interplay of topological features and disorder in periodically driven systems, using the toolkit of theoretical physics. Topological pumps, quantum walks, are some of the model systems to be explored.