SPP 1388: Representation Theory

Representation theory is a cross-disciplinary branch of mathematics with a wide range of applications in mathematics and in the sciences. Chemistry uses representation theory for instance to investigate symmetries of molecules, while quantum mechanics is a classical area of applications in physics. Further applications in physics and related areas include integrable lattice models, the theory of elementary particles, random matrix theory, string theory and quantum computing. Among the many branches of mathematics heavily using representation theory are algebraic geometry, topology, number theory and differential geometry.

Frobenius founded representation theory at the end of the 19th century when studying finite groups. At the beginning of the 20th century pioneers like Schur, Burnside, Cartan, Killing, Weyl, Noether and Brauer established fundamental concepts, objects and definitions. Today, representation theory is universally applicable and enjoys a variety of implementations; this makes representation theory truly interdisciplinary and turns it into a principle of order in mathematics and science.

Since the beginnings of representation theory, it has seen several crucial changes in points of view, in concepts and in approaches. This has led to new branches forming and to areas changing their directions. In recent years, the various branches of representation theory have started to move towards each other, and this process is increasingly gaining momentum. New methods and approaches are being formed, cutting across traditional boundaries. Innovative combinations of methods and new developments in techniques allow for deeper insights in fundamental problems and for stronger applications.

The Priority Programme will face and accept the challenge to support, promote and organise new collaborations and joint activities of different branches towards solving fundamental problems, developing new methods and applying these methods.

DFG Programme Priority Programmes

International Connection Switzerland, USA