Both stellar mass and supermassive black holes can vary in brightness extremely rapidly, changing by orders of magnitude within hours. This variability gives us a powerful tool to understand the accretion disks around black holes, and the relativistic winds that they can launch. Because the X-ray spectra are made up of multiple complex variable components, the observed variability can be strongly energy dependent. By calculating the variance of X-ray lightcurves as a function of energy, we can build a variance spectrum. These spectra have been used to qualitatively study black hole variability for many years, but are rarely used quantitatively. I will present recent results from an ongoing research program to model variance spectra of compact objects, including a new method for detecting ultra-fast outflows, implications for accretion disk physics and new constraints on AGN feedback.
Since the advent of large-area, high-quality astronomical surveys strong gravitational lensing has transitioned from a small-N to a large-N discipline. Galaxy cluster scale strong lensing, in particular, holds tremendous untapped potential. I will summarize our recent progress toward unlocking the scientific potential of large samples of strong lensing systems to address fundamental problems in astrophysics and cosmology. Focusing on recent results that highlight our sophisticated lensing analysis toolbox, I will present several pioneering measurements that lay the groundwork for future work that will use large numbers of highly magnified galaxies to answer outstanding questions about the physics of star formation and the properties of the interstellar medium in the epoch during which the Universe formed most of its stars. In addition to their value as natural telescopes, the massive structures that are responsible for the lensing action are, themselves, rare and powerful tools for testing the Lambda-CDM cosmological paradigm via the growth of structure and the mass distributions of lensing clusters.