Entering a forbidden zone

Associate Professor Sven Raum will receive funding from Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematics at Stockholm University.

Operator algebras are at the heart of the planned project. The theory of operator algebras is a relatively new field of mathematics; it was developed in the 1930s, to provide a solid mathematical foundation for the recently established quantum mechanics. Using modern operator algebras, researchers now hope to tread previously unknown territory within representation theory.

In elementary geometry, symmetries are often studied as mirror symmetries and rotational symmetries. For example, a square can be rotated through 90 degrees and two symmetries can be put together to form a new one. Together, these form a symmetry group that can be studied using algebraic methods, regardless of the geometric origin of the group. One question is whether other geometric objects can have the same symmetries and whether a list can be made of all the representations of the given symmetry group.

However, in the 1950s, American mathematician George Mackey discovered a no-go zone in representation theory, where such a list cannot be made. The way that certain special symmetry groups can actually lead from well-behaved representation theory to this forbidden no-go zone has only recently been discovered. As these symmetry groups are constructed using relatively simple concepts, there is now hope that it is possible to develop operator algebraic ideas that will surmount the current limitations in representation theory. 

Photo Martin Raum