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 Mickelsson-Faddeev) 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!
CAREER SUMMARY:
Rothmans and QEII Fellow, Dept. Math. Phys, University of Adelaide (1975-81)
Areas of expertise
Mathematical Aspects Of Classical Mechanics, Quantum Mechanics And Quantum Information Theory
Category Theory, K Theory, Homological Algebra
Operator Algebras And Functional Analysis
Mathematical Aspects Of Quantum And Conformal Field Theory, Quantum Gravity And String Theory
Interface of mathematics and quantum physics.
Mathematical questions suggested by theoretical models of low temperature conducting materials.
Topological and geometric issues that are relevant to theoretical work in quantum mechanical models.
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 Mickelsson-Faddeev) 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!
CAREER SUMMARY:
Rothmans and QEII Fellow, Dept. Math. Phys, University of Adelaide (1975-81)
Areas of expertise
Mathematical Aspects Of Classical Mechanics, Quantum Mechanics And Quantum Information Theory
Category Theory, K Theory, Homological Algebra
Operator Algebras And Functional Analysis
Mathematical Aspects Of Quantum And Conformal Field Theory, Quantum Gravity And String Theory
Interface of mathematics and quantum physics.
Mathematical questions suggested by theoretical models of low temperature conducting materials.
Topological and geometric issues that are relevant to theoretical work in quantum mechanical models.