The non-equilibrium dynamics of quantum many-body systems is a notoriously difficult topic of study, but one in which much progress is currently being made. Lieb-Robinson bounds have proven to be a valuable tool for obtaining both rigorous results and physical intuition. In this talk, after an introduction to the physical content of Lieb-Robinson bounds and a description of various applications, we discuss our recent work constructing bounds for systems with quenched disorder in 1D. We use the bounds to determine when weak links in a chain can modify the dynamical exponent (and calculate the correct dynamical exponent in such cases), and further show that even the concept of the Lieb-Robinson "light cone" must be revisited in the presence of disorder. We then close by discussing the implications of our results in numerous contexts.

(Pizza and refreshments will be served after the talk.)