Differential Geometry and Geometric Structures
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Research Areas

Present, future, and past activities: We carry out research in several areas of geometry, linking applied and pure science.

Geometric Shape Generation

Surface We aim to understand (geometric) methods, and their interrelations, to generate and design (geometric) shapes, e.g., shape generation by means of representation formulae, by transformations, kinematic generation methods, etc.

Singularity Closeness of Stewart-Gough Platforms

Linear pentapod of SG type This project is devoted to evaluating the closeness of Stewart-Gough platforms to singularities.

Spreads and Parallelisms

Spread The topic of our research are connections among spreads and parallelisms of projective spaces with areas like the geometry of field extensions, topological geometry, kinematic spaces, translation planes or flocks of quadrics.

Non-Rigidity and Symmetry Breaking

Surface We will investigate relations between non-rigidity and symmetry breaking, in particular, whether deformability in more than one way invariably leads to symmetry breaking.

Stewart-Gough Platforms with Self-Motions

Platform The main aim of the project is the systematic determination, investigation and classification of Steward-Gough platforms with self-motions.

Transformations and Singularities

Surface We aim to understand how transformations of particular surfaces behave (or fail to behave) at singularities, and to study how those transformations create (or annihilate) singularities.

Chain Geometry

Miquel The aim of the project is to investigate various aspects of the generalised chain geometry arising from the projective line over a ring which contains a (possibly skew) field.

Flexible Structures

Steffen We investigate polyhedra and frameworks which are flexible or infinitesimally flexible, and problems related to the bellows conjecture.

Line Geometry

Gauss We study differential geometric invariants of ruled surfaces, line congruences, and complexes of lines.

Descriptive Geometry

Cardano joint This is a method to study 3D geometry through 2D images. It provides insight into structure and metrical properties of spatial objects, processes and principles. We are interested in new educational tools and methodologies.

Geometry of Matrices

The aim of the project is to study projective and affine matrix spaces and related questions in the research field of linear preserver problems.

Grassmann Spaces

We exhibit the geometry and embeddings of the Grassmann space G(n,d) formed by the d-dimensional subspaces of an n-dimensional projective space over an arbitrary (skew) field F and related topics, like products of Grassmann spaces, Schubert spaces, or flag spaces.

Design Theory

Conic We investigate finite combinatorial structures, like designs and divisible designs.

Characterisations of Geometric Transformations

Ultraparallel lines Our aim is to characterise transformation groups via the invariance of a single geometric notion.

Affine Differential Geometry

Surface In affine differential geometry a main point of research is the investigation of special surfaces in three dimensional affine space.

Elementary Geometry

Altitudes of a tetrahedron For any researcher with a love of geometry, enticing problems remain.

Theory of Linear Mappings

Coordinate system The aim of this project is to discuss the mappings used in Descriptive Geometry and their generalisations from both a synthetic and analytic point of view.

Geometry of Mechanisms

Crane We are interested in flexible and in infinitesimally flexible structures - in theory as well as in applications, like gearing or the design of mechanisms for real world problems.

Veronese Varieties

Trinomial coefficients The aim of this project is to discuss Veronese varieties over a commutative ground field with non zero characteristic.

Geometry over Skew Fields

Twisted cubic We investigate reguli, Segre manifolds, normal rational curves, and their generalisations in projective spaces over arbitrary skew fields.

Geometry and Quantum Theory

Entangled qubits We exhibit, among other topics, finite geometries that describe the commutation relations between generalised Pauli operators and their Kronecker products.

Past Activities: Geometric Tolerancing, Nonlinear Subdivision, Geometric Spline Theory, Discrete Differential Geometry, Developable Surfaces

These topics can be found on the web site of Johannes Wallner, Graz University of Technology (external link).

Quick Links

33. Süddeutsches Differentialgeometrie- Kolloquium
23. Mai und 24. Mai 2008
Technische Universität Wien
(in German)


External Links: Vienna University of Technology

Faculty of Mathematics and Geo-Information: Publication Database

External Links: Institutions

FWF logo
Austrian Science Fund (FWF)

ADG logo
ADG - Fachverband der Geometrie

International Society for Geometry and Graphics

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Last modified on September 29th, 2018.