Research Projects

Our group is currently involved in the following collaborative research projects:

• SFB 647: Raum-Zeit-Materie (Space-Time-Matter)
  This is a common research project of mathematicians and physicists form universities in Berlin and Potsdam. For all projects, see the SFB Homepage. We are working on subproject C2: Differential Geometry: Geometric and Spectral Invariants of Riemannian, Lorentzian and conformal manifolds
  Abstract: The goal of the project is the study of geometric invariants of manifolds, in particular questions of their construction and classification, their properties in classes of examples and their relationship to spectral geometry. The subjects of investigation include Lorentzian manifolds with special holonomy and Lorentzian homogeneous spaces, conformal invariants and conformally covariant differential operators, the spectrum of the classical Laplace operator as well as differential operators on metric contact and CR manifolds.
  
  Finished: subproject A7: Holonomy Theory of Indefinite Metrics, Confomally Invariant Differential Operators and Q-Curvature
  Abstract: One aim of this project is to develop a theory of conformally invariant differential operators which are canonically associated to submanifolds of Riemannian manifolds and to study the structure of Q-curvature. Another goal is to develop the holonomy theory of indefinite metrics and of conformal structures, in particular to study the global geometric structure of pseudo-Riemannian manifolds with special holonomy.
• Group of Eight / DAAD: Go8 Germany Joint Research Co-operation Scheme
  Projekt: Spinor field equations in global Lorentzian geometry, together with Thomas Leistner (U Adelaide).