INTERESTS

Recently, my research has been focussed on von Neumann invariants of manifolds such as L² torsion, L² determinant lines and L² spectral flow. These are in turn related to noncommutative geometry in a semifinite von Neumann algebra. In this area I am now working on the semifinite local index formula in noncommutative geometry, its extensions and applications. I am also interested in geometric questions in quantum field theory.

In work with Michael Murray and Jouko Mickelsson, I found that the geometric significance of Hamiltonian anomalies (such as that of Mickelsson-Faddeev) is that they are invariants of bundle gerbes. Gerbes appear to arise in a number of different areas of mathematics and finding new applications of them is an ongoing interest.