| Contents:
|
Research Interests
I am in my fifth year of graduate studies and currently working on my Ph.D. thesis under the direction of Professor Xianzhe Dai. In my dissertation I explore the links between gradient Ricci solitons, warped product Einstein metrics, including static metrics in relativity, and conformally Einstein metrics. Many authors have observed a "surprising" similarity between the equations studied. Through the notion of a smooth metric measure space and generalized notions of Ricci curvature one can assign to such spaces, I have found a way to relate all of the above "quasi-Einstein" metrics, and am using it to explore how closely related they all are.
I am also interested in mathematical relativity, particularly global results such as the singularity theorems and the splitting theorem. These theorems have natural Riemannian analogs. Inspired by these, I am particularly interested in considering the Lorentzian extensions of similar theorems in Riemannian geometry.
|