Professor Astrid an Huef

Research Interests

I am part of the Operator Algebra research group.

I work in the general area of Functional Analysis, where we combine the techniques of analysis and linear algebra. The set of bounded operators on a Hilbert space has a rich algebraic structure, making it into what we call a C*-algebra. (A Hilbert space can be thought of as an infinite-dimensional Euclidean space and a bounded operator as an infinite matrix.) The famous theorem of Gelfand, Naimark and Segal from the 1940s says that every abstract C*-algebra can be represented as operators on some Hilbert space without loss of information.

C*-algebras first arose in connection with the representation theory of groups, and later played an important role in C*-algebraic models of quantum mechanics. I study C*-algebras by investigating their representations as operators on Hilbert spaces. Many of the C*-algebras that I am interested in arise from dynamical systems, and the challenge is to deduce information about the algebra from the dynamical system and vice versa. The sort of systems I'm interested in are transformation groups, groupoids, graphs and higher-rank graphs.

Opportunities for Students

If you are interested in pursuing a 4th year project, MA, MSc or PhD in Functional Analysis or a related algebraic area, please contact me and we'll discuss the possibilities.

Publications

You can view a list of my publications on MathSciNet (subscription required) and my preprints on the ArXiv.