One of the main topics of our research in the area of Differential Geometry is Infinite Dimensional Differential Geometry. Here, the geometry of manifolds is under investigation that is modelled on general locally convex vector spaces. In particular, the theory of infinite dimensional Lie groups (for example, groups of diffeomorphisms on finite dimensional manifolds) is studied. In the area of finite fimensional Differential Geometry the main research directions are the study of actions of Lie groups, as well as geometric structures of finite order and Cartan connections. This work has strong algebraic connections, for example to the theory of algebraic groups and to the representation theory of semisimple Lie groups. For more detailed information, please consult the pages of the individual member of the group

Members of the differential geometry group played an important role in the Initiativkolleg "Differential geometry and Lie groups". This was a structured PhD program supported by the University of Vienna which officially ended in November 2009. The speaker of the Kolleg was Peter W. Michor.

- Andreas Cap: Research interests. Publications.
- Stefan Haller: Publications.
- Andreas Kriegl
- Peter W. Michor: Description of Research. Research projects. Publications.
- Armin Rainer: Publications.
- Wolfgang A.F. Ruppert (Universität für Bodenkultur, Wien)
- Hermann Schichl Publications.

- Matthias Hammerl
- Katja Sagerschnig

- Martin Bauer
- Philipp Harms
- Osmar Maldonado
- Ales Navrat
- Katharina Neusser

- Stuart Armstrong
- Simon Hochgerner
- Josef Teichmann: Articles and Talks.
- Dennis Westra
- Florian Wisser