Differential geomtery of manifold with special holonomy and their calibrated submanifolds

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My research program is in differential geometry, an area of pure mathematics which studies the existence and properties of certain kinds of geometric shapes in high dimensions. Current theories of physics for very small distances and large energies (superstring theory and supergravity) require for their description some geometric shapes of dimensions 7 and 8, possessing special properties related to their curvature. These objects have also been of independent mathematical interest, because they are closely related to some strange exceptions that arise in algebra. The goal is to study the possible types of geometric shapes that can exist with these special curvature properties. This will contribute to a better understanding of the physical theories and the beautiful mathematics which is needed to describe them.