Institute Coordination
| Chairs: |
Prof. Dr. Frank Herrlich
Prof. Dr. Andreas Kirsch Prof. Dr. Enrico Leuzinger Prof. Dr. Claus-Günther Schmidt (Speaker) Prof. Dr. Wilderich Tuschmann |
| Secretariat: |
Allianz-Gebäude (05.20)
Room 4A-14 |
| Address: | University of Karlsruhe D-76128 Karlsruhe Germany |
| Office hours: | |
| Tel.: | ++49 721 608 42059 |
| Fax.: | ++49 721 608 42148 |
Workgroups
Below you will find a short introduction to the work of the research groups in our institute. More information can be found on the home pages of the individual groups.
Geometry group: Our research topics are located in the areas of Riemannian geometry, global differential geometry and geometric group theory. Currently we work on the following subjects: Symmetric spaces, Lie groups, discrete groups and group actions on manifolds, Kähler manifolds. Together with the number theory and algebraic geometry group we are active in the research program "Group actions in geometry and number theory".
We participate in the Diploma and International Master program for Mathematics. We offer courses and students' seminars on Riemannian geometry and related topics. In our research seminar we study current research topics in Riemannian geometry. The group is also responsible for the beginners' lectures on linear algebra, as well as mathematics courses for students of biology and chemistry.
Workgroup on Inverse Problems: The main area of research in this group is Inverse Problems, in particular Inverse Scattering Problems. Such problems are in general ill-posed: small errors in the given data can lead to completely wrong results. Furthermore, uniqueness of solution may not hold. The researchers of the group also treat questions of existence and uniqueness of solutions to Direct Scattering Problems as well as analyzing the numerical solution of such problems. Of particular interest in this respect are integral equation methods.
The group is responsible for the Advanced Mathematics I-III classes taught for beginning students of mechanical or chemical engineering courses. Additional lectures for mathematics students taught regularly by members of the group include Integral Euqations, Inverse Problems and Optimization Theory.
Workgroup on Convex Geometry: The focus of the research of the group is on Convex Geometry, Integral Geometry and Stochastic Geometry. Convex and Integral Geometry are connected to various mathematical disciplines such as functional analysis, optimization and discrete geometry, and in particular to Stochastic Geometry. Classical Integral Geometry investigates integral averages of geometrically relevant functionals with respect to the full motion group. The stochastic modelling of problems coming from applications motivates the study of more general groups of transformations. In particular, this leads to translative integral geometry. In the context of Convex Geometry, these developments correspond to the investigation of new geometric functionals. A central topic in the research of this workgroup are geometric and functional inequalities and related stability results. Another key aspect is the analysis of inverse geometric problems. Information about a geometric object is often available only in the form of an integral transform, or in terms of information about projections or sections of the object. Therefore an important task is the determination and reconstruction of information about the original object itself. Geometric results are also required in investigations of the group in the context of Stochastic Geometry, in particular in the analysis of geometric point processes, random tessellations and random polytopes.
Members of the group regularly offer courses on Convex Geometry, Integral Geometry and Stochastic Geometry. These courses are complemented by student's seminars and lectures provided in the framework of the workgroup on Stochastic Geometry.