Current Research Interests:
Broadly speaking, my research interests fall in the realm of Riemannian Geometry. More specifically, I work with compact manifolds that admit metrics of nonnegative sectional curvature. The largest class of known examples of such manifolds are biquotients. A biquotient is any manifold which can be expressed as a quotient of a homogeneous space by a free isometric action. Almost all known examples of manifolds of nonnegative sectional curvature are biquotients. Moreover, all homogeneous spaces are biquotients so my work also captures these important spaces. Therefore, biquotients provide us with a rich class of examples of manifolds of nonnegative sectional curvature.
My current research involves understanding the structure of certain manifolds that are built from biquotients. From this research, I hope to find new examples of manifolds that have nonnegative sectional curvature.