Riemannian manifolds with special holonomy

The subject area of this project is differential geometry. The holonomy group is a fundamental invariant of a Riemannian manifold. In modern geometry, there is much interest and activity concerning spaces having particular `symmetries'. This includes Riemannian manifolds with reduced holonomy, in particular Calabi-Yau varieties, G_2 and Spin(7) manifolds and also their calibrated submanifolds which are generalizations of minimal surfaces. One is naturally led to new interesting questions about geometrical and topological properties of the above spaces, their deformations and singularities, construction or classification of examples. The project will deal with some of the arising questions.