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Carey, Alan L. Professor

Senior Professor

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 L2 torsion, L2 determinant lines and L2 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!

Selected Publications


Impact Story


Awards And Honors


Teaching Overview


  • CAREER SUMMARY:

    Rothmans and QEII Fellow, Dept. Math. Phys, University of Adelaide (1975-81)

    Research Fellow, Institute of Advanced Studies, Australian National University (1982-1984).

    Lecturer, Senior lecturer, Department of Pure Mathematics, University of Adelaide (1985-1991).

    Associate Professor, Flinders University (1992).

    Professor of Pure Mathematics, University of Adelaide (1993-2001).

    Academic Dean, School of Mathematical and Computer Sciences, University of Adelaide, 1997-2001

    Director of the Mathematical Sciences Institute, Australian National University, 2002-2012

    Professor of Mathematics, Australian National University, February 2012- and Honorary Visiting Professor, University of Wollongong, September 2013-

     

    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

Keywords


  • 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.  

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 L2 torsion, L2 determinant lines and L2 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!

Selected Publications


Impact Story


Awards And Honors


Teaching Overview


  • CAREER SUMMARY:

    Rothmans and QEII Fellow, Dept. Math. Phys, University of Adelaide (1975-81)

    Research Fellow, Institute of Advanced Studies, Australian National University (1982-1984).

    Lecturer, Senior lecturer, Department of Pure Mathematics, University of Adelaide (1985-1991).

    Associate Professor, Flinders University (1992).

    Professor of Pure Mathematics, University of Adelaide (1993-2001).

    Academic Dean, School of Mathematical and Computer Sciences, University of Adelaide, 1997-2001

    Director of the Mathematical Sciences Institute, Australian National University, 2002-2012

    Professor of Mathematics, Australian National University, February 2012- and Honorary Visiting Professor, University of Wollongong, September 2013-

     

    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

Keywords


  • 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.  

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