| About Me | Teaching | Research | CV |
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My research interests lie broadly in the field of differential geometry. Specifically, my thesis research is focused on quasi-Einstein metrics, which are a useful generalization of Einstein metrics, and are of interest in relativity. Specifically, near horizon geometries are a special case of quasi-Einstein metrics.
One of my main research results, proved in my first publication below, is a characterization of when a closed quasi-Einstein metric has constant scalar curvature. This characterization has proved to be very useful in studying and classifying quasi-Einstein metrics of constant scalar curavature. I am currently working on a project which uses my characterization to classify closed quasi-Einstein metrics in the three dimensional case, and to study metrics which can be constructed as circle bundles over an Einstein base.
Outside of my thesis research, I am currently involved in a collarborative project with Arseny Mingajev, Lawrence Mouillé, and Nazia Valiyakath in which we are studying Ricci flow on homogeneous spaces. Specifcally, we are interested in studying how curvature properties are preserved under the Ricci flow in the case where there are two equivalent isotropy summands.