Research Overview

My research is now mostly about semifinite noncommutative geometry and its extensions and applications. I have been motivated by von Neumann invariants of manifolds such as L^{2} torsion, L^{2} determinant lines and L^{2} spectral flow. Currently this involves generalising the semifinite local index formula in noncommutative geometry and applying it.
Geometric questions from Quantum Field Theory are another interest. In work with Michael Murray and Jouko Mickelsson, I found that the geometric significance of Hamiltonian anomalies (such as that of MickelssonFaddeev) is that they are invariants of bundle gerbes. Recently gerbes and other twisted geometric objects have been found to arise in a number of places in string theory. There is still a lot to do!