My students and I study active earthquake and volcanic process through data collection, inversion, and theoretical modeling. Using methods such as precise Global Positioning System (GPS) positioning and Interferometric Synthetic Aperture Radar (InSAR) we are able to measure deformation in space and time and invert these data for the geometry of faults and magma chambers, and spatiotemporal variations in fault slip-rate and magma chamber dilation. The accumulation of shear strain in tectonic regions provides a direct measure of earthquake potential. Similarly, magma accumulation in the crust prior to eruptions causes measurable inflation. We use these data to develop and test models of active plate boundaries such as the San Andreas, and the Cascade and Japanese subduction zones, the nucleation of earthquakes, slow slip events, induced seismicity, and the physics of magma migration leading to volcanic eruptions. These physics-based models rely on principles and methodologies from solid and fluid dynamics.