I am a post-doctoral lecturer in the Department of Mathematics at the University of Pennsylvania. I received my Ph.D. in May 2010 from Duke University under the direction of Hubert Bray. Prior to that, I received my bachelor's degree from Harvey Mudd College.
Broadly speaking, my research is in the fields of differential geometry and general relativity. Einstein's theory of general relativity asserts that space and time should be understood through their geometry, particularly their curvature. In Riemannian geometry, scalar curvature is interesting to study because it is arguably the simplest local Riemannian invariant. In general relativity, scalar curvature is intimately connected with energy density. Inspired by such physical considerations, a number of results in geometric analysis, such as the positive mass theorem and Riemannian Penrose inequality, have global implications for manifolds of nonnegative scalar curvature.
The over-arching goal of my research is to better understand the geometry of manifolds of nonnegative scalar curvature, including manifolds that may have singularities. I am also interested in quasi-local mass/energy and static metrics.
