Research Interests : Quantum Field Theory.
Professor Carey's recent research has focused on von Neumann invariants of manifolds such as LČ torsion, LČ determinant lines and LČ spectral flow. These are in turn related to noncommutative geometry in a semifinite von Neumann algebra. He has also been interested in geometric questions in quantum field theory.
In work with Mickael Murray and Jouko Mickelsson, he 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 on-going interest.
Awards and Honors : University medal for Pure Mathematics (1972)
Commonwealth Overseas Scholarship (1972-1975)
Rothmans Fellowship (1975-1977)
Queen Elizabeth II Fellowship (1978-79)
Prizes Fund Visiting Fellow, Oxford University; 1991, 1998, 2000
Distinguished Visiting Scientist, Victoria University, Canada; 1988
CMI Scholar; September 2000 and July-September, 2001
Selected Publications : Journal Articles :
"On unbounded p-summable Fredholm modules", (A.L. Carey, J. Phillips, F. Sukochev), Advances in Mathematics, 151 (2000), 140-163
"Correspondences, von Neumann algebras and holomorphic L2 torsion", (A.L. Carey, M. Farber, V. Mathai), Canadian Journal of Mathe matics Vol 52 No. 4 (2000), 695-736
"Cuntz algebras and quantum groups", (A.L. Carey, A. Paolucci, R. Zhang), Annales Inst. Henri Poincare, to appear.
"A gerbe obstruction to quantisation of fermions on odd-dimensional manifolds with boundary", (A.L. Carey, J. Mickelsson), Lett Math Phys, to a ppear
"Seiberg-Witten-Floer homology and gluing theorems", (A.L. Carey, B-L. Wang), Asian Journal of Mathematics, to appear
Books Edited :
"Confronting the Infinite", (Eds: A.L. Carey, W. Ellis, P.A. Pearce, A.W. Thomas), World Scientific, 1995.
Australian Mathematical Society Lecture Series, "Algebraic groups and Related Subjects: a Volum in Honour of R. W. Richardson", (Eds: G.I. Lehrer with A.L. Carey, T. Carroll, M.K. Murray, T. Springer), Cambridge University Press, 1996.
Australian Mathematical Society Lecture Series, "Geometric analysis and lie theory in Mathematics and Physics" (Eds: A.L. Carey and M.K. Murray), Camb ridge University Press, 1998.