Manifolds with reduced holonomy.

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The subject area of proposed research is differential geometry and global analysis. The holonomy group is a fundamental invariant of a Riemannian manifold. In recent years, there has been much interest in `special geometries' arising e.g. in Calabi--Yau, G_2 and Spin(7) manifolds from considerations of holonomy reduction or restrictions on the curvature and also their `calibrated' minimal submanifolds. These structures may often be expressed as solutions of geometrically natural non-linear and elliptic partial differential equations. There is a number of important open questions concerning general geometric and topological properties of the latter manifolds, their deformations and singularities, as well as construction and classification of examples. The PhD project will deal with research tasks motivated by some of these open questions.