My research area is geometric analysis, specifically the study of critical metrics in dimension four and its applications to topology and geometry. I am particularly interested in problems in conformal geometry that involve looking at higher order (fourth order and higher) degenerate elliptic equations. One example of these problems is given by the study of Bach-flat metrics, which are metrics that are critical to a functional closely related to the Gauss-Bonnet formula in dimension four. Bach-flat metrics satisfy a fourth order system of equations that has conformal properties.
