Imaging the Horizons of Black Holes
You can read more in a recent article I co-authored for the September 2015 special issue of Scientific American on the 100th anniversary of the Theory of General Relativity
Testing General Relativity Across Different Scales
General Relativity has been subjected to numerous experimental tests, mostly in the weak gravitational fields found in our Solar System and has passed all of them with flying colors. In contrast, gravity in the strong-field regime and at cosmological settings has been largely unconstrained by experiments, with only limited studies around neutron stars in binaries and using cosmological structure formation. A large class of gravity theories can be constructed that obey the Einstein equivalence principle and cannot be rejected by solar system tests, but that diverge from general relativity in other regimes. Our aim is to explore how tests of General Relativity at different scales can be compared and contrasted, as well as to design new tests of the theory that span different scales.
You can find more information in this technical article I wrote for the online journal Living Reviews in Relativity
Magnetohydrodynamic Turbulence in Shearing Flows
Differentially rotating magnetohydrodynamic flows exhibit a number of instabilities. Some of these are believed to be responsible for generating and sustaining turbulence that allows black holes and neutron stars to accrete matter at high rates and become powerful X-ray sources in the sky. We are studying the onset and the outcome of magnetohydrodynamic turbulence, using analytical and numerical tools.