The Ross Group at the California Institute of Technology studies all aspects of earthquakes, fault zones, and the hazards they pose to society. Our research focuses on high-resolution imaging of fault zones; understanding the rich patterns formed by earthquake sequences in space and time; resolving details of the earthquake source process over a time scale of seconds; characterizing the expected ground shaking during large, damaging earthquakes; and using all of these observations together to constrain the structural and mechanical properties of fault zones at depth. To achieve these goals, we develop and incorporate algorithms from machine learning and applied/computational mathematics to extract hidden signals from the largest seismic datasets.