Recent work on topological materials has revealed a wide variety of intriguing phenomena that may arise when particles move in "non-trivial" bands. At the same time, modern advances in experimental capabilities for controlling electronic, atomic, and optical systems open new possibilities for dynamically controlling the behaviors of a range of quantum systems. In this talk I will review the basic ideas behind topological band theory, and then explain how periodic driving can be used to gain dynamical control over the topological properties of quantum matter. In the driven case, intriguing new types of robust non-equilibrium topological phenomena emerge. To illustrate, I will show how the combination of driving, topology, and interactions can bring about a new regime of universal quantized transport, and discuss potential near-term experimental realizations.
**THE RECEPTION WILL BE HELD AT 3:00PM IN ROOM 313**