This research group covers a wide variety of interests and topics, ranging from classical differential geometries of various flavours to more abstract geometric structures and modern geometric methods, as well as relations with other sciences and applications of geometry.
The focus of our work is on fundamental research with relations to theoretical physics and underpinning applications rather than on immediate applications though, for example, work on “Stewart Gough platforms” relates fairly directly to applications in robotics. For example, theoretical research on transformations and metamorphoses of surfaces leads to results on facetted and panelled surfaces, which are relevant in computer graphics and computational design as well as in architectural applications.
The group is internationally well connected, most notably through a recent Joint Project with Japanese institutions in Fukuoka, Tokyo and Kobe, involving about twenty researchers from Austria and Japan.
Singularity Closeness of Stewart-Gough Platforms
Motion Platform Optimization
Transformations and Base Shape Analysis
Geometric Shape Generation
Discrete curvature and rigidity
Kokotsakis polyhedra: Analysis of foldable structures