I will summarize recent work on the quantum speed limit in time independent closed systems. I will then go on to describe the way these results extend to the time dependent regime, and thus to quantum control. Differential geometry has been a vital tool in control theory in general for some time, particularly of note is the application of geodesic equations to time optimal control. I will discuss applications of differential geometry to quantum time optimal control and recent speed limit results obtained by myself and others. Finally, discussion about the outlook for these types of methods in general compared to their alternatives will be presented.
(PLEASE NOTE NON-STANDARD LOCATION)