The International Research Training Group “Geometry and Analysis of Symmetries” (IRTG) is a doctoral education program run by the universities of Paderborn and Metz (France), designed to catalyze the interaction between specialists in diverse fields. It also aims to bring master students to a level where they can actively participate in this cooperation. The team brings expertise from unitary representations, symplectic and non-commutative geometry and non-commutative harmonic analysis on the one hand, and homological algebra, microlocal analysis, function spaces and C*-algebras on the other hand. This type of research requires interdisciplinary cooperation and the use of a variety of tools from other mathematical disciplines, making it a fascinating and fruitful area for further study.
Students are expected to have developed an interest in at least one of the subject areas the IRTG focuses on. Doctoral students are actively supported in gaining proficiency in other relevant mathematical disciplines through self-study, professor support, further courses, and student interaction. Students are also actively supported in their research, through frequent informal interaction with professors and an extensive international network of colleagues. Students typically spend half the year in Metz and the other half in Paderborn, thereby profiting from two research groups and two academic cultures.
Research areas of the IRTG are:
Arithmetic geometry (Prof. Wedhorn)
Quantum groups and deformation quantization (Dr. Bonneau)
Function spaces, Fréchet spaces, and topological tensor products (Prof. Bierstedt)
Harmonic analysis on symmetric spaces, special functions (Prof. Pasquale)
Infinite dimensional geometry (Prof. Glöckner)
Microlocal analysis (Prof. Hansen)
Non-commutative geometry, Baum-Connes conjecture and twisted K-theory (Prof. Tu)
Non-commutative geometry, index theory, and quasi-crystals (Prof. Benameur)
Deformation quantization and star products (Dr. Chloup)
Representation theory of finite dimensional algebras (Prof. Krause)
Representation theory of solvable Lie groups and convolution algebras of locally compact groups (Prof. Ludwig)
Symplectic and complex geometry, infinite dimensional manifolds and Lie groups, mathematical theory of classical and quantum field theory (Prof. Wurzbacher)
Representation theory of Lie groups and applications (Prof. Mehdi)
Unitary representations and harmonic analysis (Prof. Hilgert)
Harmonic analysis, homogenous spaces and C*-algebras (Dr. Prudhon)
The International Research Training Group "Geometry and Analysis of Symmetries" is one of five such groups initiated and supported by the Deutsche Forschungsgemeinschaft (DFG), the French Ministry of Education, Science and Research (MENESR) and the Franco-German University (DFH-UFA).
The IRTG PhD-programm "Structures with Symmetries" is accepted by the DAAD to be included into the new bi-national PhD-Network (PhD-Net).