# Research Topics

Geometry as a classical mathematical discipline plays an important role in our current time. Omnipresent computer visualizations, analysis and representations of big data and geometric shapes in modern architecture are only some examples highlighting the increasingly important role of geometric research questions. Geometry as a mathematical discipline is challenged by that fact that it is on the one hand an area of strict mathematical logic but on the other hand emphazises visual and diagrammatic thinking.

A special emphasis in our research groups lies in the algorithmic treatment of geometric structures. Areas reach from fundamental data structures, via visualization, and data analysis to the simulation of dynamical systems. In particular, we consider ourselves as closely connected to adjacent areas like algebra, combinatorics, optimisation, dynamical systems and many more.

A further interest of our group lies in communication of mathematics to a general public. In that context many activities like the mathematics exhibition ix-quadrat, the development of visualization software and the collaboration with other exhibitions are located in our group as well.

### Geometry and Visualization

The research group around Prof. Jürgen Richter-Gebert deals with topics related to computer oriented visualization of mathematical structures. Research topics range from mathematical foundations via implementation of authoring systems to the visualization of concrete content.

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### Computational Topology

The research group around Prof. Ulrich Bauer deals with the computational analysis of topological structures arising in real world data.

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### Discrete Differential Geometry

The research group around Prof. Tim Hoffmann deals the structure preserving discretisation of continuous phenomena in differential geometry.

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