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Research Interests

My research is on the geometry of minimal submanifolds. Specifically, I am investigating some rigidity problems for closed minimal submanifolds of products of spheres, and of reducible symmetric spaces. This draws upon the work of James Simons, who gave similar results for submanifolds of spheres. Specifically, in a product of spheres, the factors are rigid when considered among minimal submanifolds.

I am also interested in calibrated geometry. This is an additional structure on a Riemannian manifold induced by a closed differential form. Important examples are Kaehler manifolds, symmetric spaces and other manifolds with reduced holonomy. I am interested in a geometric flow that can be defined on 3-dimensional submanifolds of manifolds with holonomy contained in the group G_2. The fixed points of the flow are the submanifolds calibrated by the associative form.