Professor Alan Carey
BSc (Sydney), MSc (Adelaide), DPhil (Oxford)
Professor of Mathematics
ANU College of Science
Areas of expertise
- Mathematical Aspects Of Classical Mechanics, Quantum Mechanics And Quantum Information Theory 010503
- Category Theory, K Theory, Homological Algebra 010103
- Operator Algebras And Functional Analysis 010108
- Mathematical Aspects Of Quantum And Conformal Field Theory, Quantum Gravity And String Theory 010505
Publications
- Bourne, C, Carey, A, Lesch, M et al. 2022, 'The KO-valued spectral flow for skew-adjoint Fredholm operators', Journal of Topology and Analysis, vol. 14, no. 2, pp. 505-556.
- Carey, A & Thiang, G 2021, 'The Fermi gerbe of Weyl semimetals', Letters In Mathematical Physics, vol. 111, no. 72.
- Carey, A, Phillips, J & Schulz-Baldes, H 2019, 'Spectral flow for skew-adjoint Fredholm operators', Journal of Spectral Theory, vol. 9, no. 1, pp. 137-170.
- Carey, A & Schulz-Baldes, H 2019, 'Spectral Flow of Monopole Insertion in Topological Insulators', Communications in Mathematical Physics, vol. 370, no. 3, pp. 895-923.
- Carey, A, Gesztesy, F, Kaad, J et al 2018, 'On the Global Limiting Absorption Principle for Massless Dirac Operators', Annales Henri Poincare, vol. 19, no. 7, pp. 1993-2019.
- Carey, A, Gesztesy, F, Potapov, D et al 2017, 'On the Witten index in terms of spectral shift functions', Journal d'Analyse Mathematique, vol. 132, no. 1, pp. 1-61.
- Carey, A & Kaad, J 2017, 'Topological invariance of the homological index', Journal fur Reine und Angewandte Mathematik (Crelles Journal), vol. 729, no. 729, pp. 229-261.
- Bourne, C, Carey, A & Rennie, A 2016, 'A non-commutative framework for topological insulators', Reviews in Mathematical Physics, vol. 28, no. 2.
- Carey, A, Gesztesy, F, Grosse, H et al 2016, 'Trace formulas for a class of non-Fredholm operators: A review', Reviews in Mathematical Physics, vol. 28, no. 10, pp. 47pp.
- Carey, A, Rennie, A, Sukochev, F et al 2016, 'Universal measurability and the Hochschild class of the Chern character', Journal of Spectral Theory, vol. 6, no. 1, pp. 1-41.
- Carey, A, Gesztesy, F, Levitina, G et al 2016, 'Double operator integral methods applied to continuity of spectral shift functions', Journal of Spectral Theory, vol. 6, no. 4, pp. 747-779.
- Carey, A, Gesztesy, F, Levitina, G et al 2016, 'On the index of a non-Fredholm model operator', Operators and Matrices, vol. 10, no. 4, pp. 881-914pp.
- Carey, A, Grosse, H & Kaad, J 2016, 'On a spectral flow formula for the homological index', Advances in Mathematics, vol. 289, pp. 1106-1156.
- Carey, A, Gesztesy, F, Levitina, G et al 2016, 'On index theory for non-Fredholm operators: A (1+1)-dimensional example', Mathematische Nachrichten, vol. 289, no. 5-6, pp. 575-609.
- Bourne, C, Carey, A & Rennie, A 2016, 'A non-commutative framework for topological insulators', Reviews in Mathematical Physics, vol. 28, no. 2.
- Carey, A, Gesztesy, F, Levitina, G et al 2016, 'The spectral shift function and the Witten index', Operator Theory: advances and applications, vol. 254, pp. 71-105.
- Carey, A, Gayral, V, Phillips, J et al 2015, 'Spectral Flow for Nonunital Spectral Triples', Canadian Journal of Mathematics, vol. 67, no. 4, pp. 759-794.
- Bourne, C, Carey, A & Rennie, A 2015, 'The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory', Letters In Mathematical Physics, vol. 105, no. 9, pp. 1253-1273.
- Carey, A, Grosse, H & Kaad, J 2015, 'Anomalies of Dirac Type Operators on Euclidean Space', Communications in Mathematical Physics, vol. 335, no. 1, pp. 445-475.
- Bourne, C, Carey, A & Rennie, A 2015, 'The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory', Letters In Mathematical Physics, vol. 105, no. 9, pp. 1253-1273.
- Carey, G, Malbon, E, Carey, N et al 2015, 'Systems science and systems thinking for public health: a systematic review of the field', BMJ Open 2015;5:e009002 doi:10.1136/bmjopen-2015-009002
- Carey, A, Gesztesy, F, Potapov, D et al 2014, 'A Jost-Pais-Type Reduction of Fredholm Determinants and Some Applications', Integral Equations and Operator Theory, vol. 79, no. 3, pp. 389-447.
- Carey, A, Gayral, V, Rennie, A et al 2014, Index theory for locally compact noncommutative geometries, American Mathematical Society, Providence, USA.
- Benameur, M & Carey, A 2013, 'Higher spectral flow and an entire bivariant JLO cocycle', Journal of K-Theory, vol. 11, no. 1, pp. 183-232.
- Baum, P, Carey, A & Wang, B 2013, 'K-cycles for twisted K-homology', Journal of K-Theory, vol. 12, no. 1, pp. 69-98.
- Bouwknegt, P, Carey, A & Ratnam, R 2013, 'Recent Advances in the Study of the Equivariant Brauer Group', K-Theory and D-Branes, ed. Giuseppe Dito, World Scientific Publishing Co. Pte Ltd, Singapore, pp. 335-358.
- Carey, A, Phillips, J & Rennie, A 2013, 'Semi-Finite Noncommutative Geometry and some applications', K-Theory and D-Branes, ed. Giuseppe Dito, World Scientific Publishing Co. Pte Ltd, Singapore, pp. 37-58.
- Carey, A, Phillips, J, Rennie, A et al 2013, 'The local index formula in noncommutative geometry revisited', K-Theory and D-Branes, ed. Giuseppe Dito, World Scientific Publishing Co. Pte Ltd, Singapore, pp. 3-36.
- Carey, A & Sukochev, F 2012, 'Measurable operators and the asymptotics of heat kernels and zeta functions', Journal of Functional Analysis, vol. 262, no. 10, pp. 4582-4599.
- Carey, A, Gayral, V, Rennie, A et al 2012, 'Integration on locally compact noncommutative spaces', Journal of Functional Analysis, vol. 263, no. 2, pp. 383-414.
- Carey, A, Bouwknegt, P & Lohe, M 2012, 'Obituary: Charles Angas Hurst, AM FAA', Australian Mathematical Society Gazette, vol. 39, no. 1, pp. 30-32.
- Carey, A, Phillips, J & Rennie, A 2011, 'Spectral triples: examples and index theory', in Alan Carey (ed.), Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory, European Mathematical Society Publishing House, Zurich, pp. 175-265pp.
- Carey, A, Neshveyev, S, Nest, R et al. 2011, 'Twisted cyclic theory, equivariant KK-theory and KMS states', Journal fur Reine und Angewandte Mathematik (Crelles Journal), vol. 650, pp. 161-191.
- Carey, A, Phillips, J, Putnam, I et al. 2011, 'Families of type III KMS states on a class of C*-algebras containing On and QN', Journal of Functional Analysis, vol. 260, no. 6, pp. 1637-1681.
- Carey, A & Wang, B 2010, 'Riemann-Roch and index formulae in twisted K-theory', Symposia in Pure Mathematics 2010, American Mathematical Society, USA, pp. 95-132.
- Carey, A, Klimek, S & Wojciechowski, K 2010, 'A dirac type operator on the non-commutative disk', Letters In Mathematical Physics, vol. 93, no. 2, pp. 107-125.
- Carey, A, Phillips, J & Rennie, A 2010, 'Noncommutative Atiyah-Patodi-Singer boundary conditions and index pairings in KK-theory', Journal fur Reine und Angewandte Mathematik (Crelles Journal), vol. 643, pp. 59-109.
- Carey, A, Phillips, J & Rennie, A 2010, 'Twisted cyclic theory and an index theory for the gauge invariant KMS state on the Cuntz algebra On', Journal of K-Theory, vol. 6, no. 2, pp. 339-380.
- Carey, A, Rennie, A & Tong, K 2009, 'Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2)', Journal of Geometry and Physics, vol. 59, no. 10, pp. 1431-1452.
- Carey, A, Wang, B & Mickelsson, J 2009, 'Differential twisted K-theory and applications', Journal of Geometry and Physics, vol. 59, pp. 632-653.
- Carey, A, Potapov, D & Sukochev, F 2009, 'Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators', Advances in Mathematics, vol. 222, no. 5, pp. 1809-1849.
- Carey, A & Benameur, M 2009, 'On the analyticity of the bivariant JLO cocycle', Electronic Research Announcements in Mathematical Sciences, vol. 16, pp. 37-43.
- Azamov, N, Carey, A, Dodds, P et al 2009, 'Operator Integrals, Spectral Shift, and Spectral Flow', Canadian Journal of Mathematics, vol. 61, no. 2, pp. 241-263.
- Carey, A, Phillips, J & Rennie, A 2008, 'Semifinite spectral triples associated with graph C*-algebras', in S. Albeverio, M. Marcolli, S Paycha, J Plazas (ed.), Traces in Number Theory, Geometry and Quantum Fields, Vieweg, Germany, pp. 35-56.
- Carey, A & Wang, B 2008, 'Thom isomorphism and push-forward map in twisted K-theory', Journal of K-Theory, vol. 1, no. 2, pp. 357-393.
- Carey, A & Wang, B 2008, 'Fusion of Symmetric D-Branes and Verlinde Rings', Communications in Mathematical Physics, vol. 277, no. 3, pp. 577-625.
- Carey, A, Phillips, J, Rennie, A et al 2008, 'The Chern character of semifinite spectral triples', Journal of Noncommutative Geometry, vol. 2, no. 2, pp. 141-193.
- Azamov, N, Carey, A & Sukochev, F 2007, 'The spectral shift function and spectral flow', Communications in Mathematical Physics, vol. 276, no. 1, pp. 51-91.
- Carey, A 2007, 'Semi-finite noncommutative geometry and invariants from KMS states', Nichtkommutative Geometrie Workshop, ed. Gert-Martin Greuel, European Mathematical Society Publishing House, Switzerland.
- Carey, A, Rennie, A, Sedaev, A et al 2007, 'The Dixmier trace and asymptotics of zeta functions', Journal of Functional Analysis, vol. 249, pp. 253-283.
- Carey, A & Sukochev, F 2006, 'Dixmier traces and some applications in noncommutative geometry', Russian Mathematical Surveys, vol. 61, no. 6, pp. 1039-1100.
- Carey, A, Phillips, J, Rennie, A et al 2006, 'The local index formula in semifinite Von Neumann algebras I: Spectral flow', Advances in Mathematics, vol. 202, pp. 451-516.
- Benameur, M, Carey, A, Phillips, J et al 2006, 'An Analytic Approach to Spectral Flow in von Neumann Algebras', in Booss-Bavnbek, Klimek, Lesch, Zhang (ed.), Analysis, Geometry and Topology of Elliptic Operators, World Scientific Publishing Company, Singapore, p. 56.
- Carey, A 2006, 'Examples of odd index theorems', Reports on Mathematical Physics, vol. 57, no. 1, pp. 41-51.
- Carey, A, Phillips, J, Rennie, A et al 2006, 'The local index formula in semifinite von Neumann algebras II: the even case', Advances in Mathematics, vol. 202, pp. 517-554.
- Carey, A & Wang, B 2006, 'On the relationship of gerbes to the odd families index theorem', Journal of Geometry and Physics, vol. 57, pp. 23-38.
- Carey, A, Hannabuss, K, Mathai, V et al 2006, 'Quantum Hall effect and noncommutative geometry', Journal of Geometry and Symmetry in Physics, vol. 6, pp. 16-37.
- Carey, A, Johnson, S, Murray, M et al. 2005, 'Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories', Communications in Mathematical Physics, vol. 259, no. 3, pp. 577-613.
- Carey, A, Johnson, S, Murray, M et al 2005, 'Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories', Communications in Mathematical Physics, vol. 259, pp. 577-613.
- Braverman, M, Carey, A, Farber, M et al 2005, 'L2 torsion without the determinant class condition and extended L2 cohomology', Communications in Contemporary Mathematics, vol. 7, no. 4, pp. 421-462.
- Carey, A & Grundling, H 2004, 'On the problem of the amenability of the gauge group', Letters In Mathematical Physics, vol. 68, pp. 113-120.
- Carey, A, Johnson, S & Murray, M 2004, 'Holonomy on D-branes', Journal of Geometry and Physics, vol. 52, pp. 186-216.
- Carey, A, Phillips, J, Rennie, A et al 2004, 'The Hochschild class of the Chern character for semifinite spectral triples', Journal of Functional Analysis, vol. 213, pp. 111-153.
- Carey, A & Phillips, J 2004, 'Spectral Flow in Fredholm Modules, eta invariants and the JLO Cocycle', K-Theory, vol. 31, pp. 135-194.
- Carey, A, Phillips, J & Sukochev, F 2003, 'Spectral flow and Dixmier traces', Advances in Mathematics, vol. 173, pp. 68-113.
- Carey, A, Marcolli, M & Wang, B 2003, 'The geometric triangle for 3-dimensional Seiberg-Witten monopoles', Communications in Contemporary Mathematics, vol. 5, pp. 197-250.
- Carey, A & Wang, B 2003, 'Seiberg-Witten-Floer homology and gluing formulae', Acta Mathematica Sinica, vol. 19, no. 2, pp. 245-296.
- Carey, A & Wang, B 2003, 'Seiberg-Witten-Floer homology and gluing formulae', Acta Mathematica Sinica, vol. 19, no. 2, pp. 245-296.
- Carey, A, Marcolli, M & Wang, B 2003, 'The geometric triangle for 3-dimensional Seiberg-Witten monopoles', Communications in Contemporary Mathematics, vol. 5, no. 2, pp. 197-250.
- Carey, A & Mickelsson, J 2002, 'The Universal Gerbe, Dixmier-Douady classes and gauge theory', Letters In Mathematical Physics, vol. 59, pp. 47-60.
- Bouwknegt, P, Carey, A, Mathai, V et al. 2002, 'Twisted K-theory and K-Theory of Bundle Gerbes', Communications in Mathematical Physics, vol. 228, no. 1, pp. 17-49.
- Carey, A & Baumgaertel, H 2001, 'Hilbert C*-systems for actions of the circle group', Reports on Mathematical Physics, vol. 47, pp. 145-160.
Projects and Grants
Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.
- New methods in spectral geometry. (Secondary Investigator)
- The boundaries of index theory (Secondary Investigator)
- Novel geometric constructions (Primary Investigator)
- Noncommutative analysis and geometry in interaction with quantum physics (Secondary Investigator)
- Invariants of singular spaces from noncommutative geometry (Primary Investigator)
- Algebraic invariants in mathematics and physics (Primary Investigator)
- Geometric problems from quantum theory (Secondary Investigator)