Project Details
Projekt
GRK 1133: Geometry and Analysis for Symmetries
Subject Area
Mathematics
Term
from 2005 to 2010
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 776961
The analysis of systems with symmetries involves a number of different mathematical fields from representation theory and harmonic analysis, the theory of integral transformations, symplectic/complex and non-commutative geometry as well as infinite dimensional differential geometry and quantisation. Even though many central questions in the analysis of symmetries are still open, their study has produced a wealth of deep results with very diverse applications to fields such as partial differential equations, mathematical physics, number theory, ergodic theory, complex analysis, and index theory.
This International Research Training Group (IRTG) is designed to meet the challenge of catalysing cooperation between specialists in these diverse fields and at the same time to bring beginners up to a level where they can actively contribute to this cooperation. The team of researchers involved consists on the one hand of experts in unitary representations, non-commutative harmonic analysis and microlocal analysis, and on the other hand of specialists in fields like homological algebra, function spaces, C*-algebras and symplectic and non-commutative geometry. The basic idea of the research programme is to combine the expertise in these neighbouring but distinct fields to attack a variety of problems which were either too hard to be solved by techniques from a single field or, because of their interdisciplinary character, have failed to attract the attention they deserve.
The cooperation in teaching and research between the two departments involved will be based on joint seminars and workshops as well as frequent exchange visits of teachers and students. In addition, detailed study material will be produced and made available to all partners.
The students will earn a joint degree. Whereas research cooperation can follow well established procedures, the teaching cooperation will have to try out new concepts. The goal is to develop procedures that can serve as models also for other projects. The interest of neighbouring institutions to participate in summer schools of the IRTG shows that there is potential in this direction.
This International Research Training Group (IRTG) is designed to meet the challenge of catalysing cooperation between specialists in these diverse fields and at the same time to bring beginners up to a level where they can actively contribute to this cooperation. The team of researchers involved consists on the one hand of experts in unitary representations, non-commutative harmonic analysis and microlocal analysis, and on the other hand of specialists in fields like homological algebra, function spaces, C*-algebras and symplectic and non-commutative geometry. The basic idea of the research programme is to combine the expertise in these neighbouring but distinct fields to attack a variety of problems which were either too hard to be solved by techniques from a single field or, because of their interdisciplinary character, have failed to attract the attention they deserve.
The cooperation in teaching and research between the two departments involved will be based on joint seminars and workshops as well as frequent exchange visits of teachers and students. In addition, detailed study material will be produced and made available to all partners.
The students will earn a joint degree. Whereas research cooperation can follow well established procedures, the teaching cooperation will have to try out new concepts. The goal is to develop procedures that can serve as models also for other projects. The interest of neighbouring institutions to participate in summer schools of the IRTG shows that there is potential in this direction.
DFG Programme
International Research Training Groups
International Connection
France
Applicant Institution
Universität Paderborn
IRTG-Partner Institution
Université de Lorraine
Spokesperson
Professor Dr. Joachim Hilgert
Participating Researchers
Privatdozent Dr. Alexander Alldridge; Professor Dr. Sönke Hansen; Andrew Hubery, Ph.D.; Professor Dr. Henning Krause
