DFF grant for Mikael Rørdam

Mikael Rørdam is professor and Deputy Head of Department for Research at the Department of Mathematical Sciences. Mikael describes his project like this:

Operator algebras are by definition algebras of operators on a Hilbert space, and they originally were developed in the 1930s and 40s as the mathematical framework for quantum mechanics.

This project is about C*-algebras, which on the one hand are operators on a Hilbert space and on the other hand can be viewed as, and behave like, non-commutative topological spaces.

Taking the point of view of the latter interpretation, one can (in more than one way) associate a dimension to a C*-algebra; one of them, developed by Rieffel in the early 1980s, called stable rank, is likely the most enigmatic. The outstanding question of deciding when simple (i.e., indecomposable) C*-algebras have the lowest possible stable rank (namely one) has seen a revival over the last years, fueled by the renewed interest in understanding (simple) C*-algebras arising from groups and dynamical systems, following the succesful recent classificaion of (a certain class of) simple C*-algebras.

By blending techniques from geometric group theory and from C*-algebras one main goal of the project is to compute the dimension of simple C*-algebras arising from groups.

The DFF grant will fund a postdoc who will bring in complementary knowledge to address this and related problems.