NONTECHNICAL SUMMARY Electrons are very light and move very fast in materials: if one tries to drive them out of their equilibrium steady state, for example by using an applied voltage, they reorganize rapidly and establish a new steady state. Until very recently, experimenters were incapable of measuring materials on fast-enough timescales to see how electrons behave when they are far out of equilibrium before they reach a new steady state. This restriction to studying electrons in materials at or near equilibrium has fundamentally limited understanding of the physical mechanisms governing charge and heat conduction, magnetism, and other topics. In the past decade, developments in ultrafast laser technology have made it possible to study far-from-equilibrium systems of electrons. Apart from isolated examples, however, there is no theoretical framework for interpreting such experiments, i.e., for understanding what they can tell us about the underlying quantum mechanical dynamics of the electrons, or how we can use this knowledge to guide the search for materials with new functionalities. This is the theoretical gap that the present project aims to fill. This project has two main thrusts. First, for broad classes of systems — such as superconductors and thin wires — the researchers will develop explicit predictions for out-of-equilibrium behavior based on state-of-the-art theoretical descriptions. In materials that exhibit exotic phenomena, there are often multiple t