World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
36
Citations
4492
World Ranking
2680
National Ranking
60

Research.com Recognitions

  • 2014 - Fellow of the Australian Academy of Science

Overview

Alan L. Carey is affiliated with the Australian National University in Australia and has contributed extensively to the fields of Mathematics, Computer Science, and Physics and Astronomy. Their research focuses on subfields such as Mathematical Physics, Applied Mathematics, Computational Theory and Mathematics, Atomic and Molecular Physics and Optics, and Geometry and Topology.

The scientist has published numerous works in topics including Spectral Theory in Mathematical Physics, Advanced Operator Algebra Research, Matrix Theory and Algorithms, Topological Materials and Phenomena, Holomorphic and Operator Theory, Mathematical Analysis and Transform Methods, and Quantum many-body systems.

Recent publications by Alan L. Carey include:

  • The KO-valued spectral flow for skew-adjoint Fredholm operators, 2020, Journal of Topology and Analysis
  • The Witten index and the spectral shift function, 2022, Reviews in Mathematical Physics
  • The product formula for regularized Fredholm determinants, 2021, Proceedings of the American Mathematical Society Series B
  • The limiting absorption principle for massless Dirac operators, properties of spectral shift functions, and an application to the Witten index of non-Fredholm operators, 2021, arXiv (Cornell University)
  • On a conjectured property of the Witten index and an application to Levinson's theorem, 2023, arXiv (Cornell University)

Frequent co-authors include Galina Levitina, Fedor Sukochev, Fritz Gesztesy, Dmitriy Zanin, and Roger Nichols.

Alan L. Carey has also contributed to book publications:

  • The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators, published by Memoirs of the European Mathematical Society, 2023
  • Index Theory Beyond the Fredholm Case, published by Springer Nature, 2022

Publications have appeared in various venues, notably arXiv (Cornell University), Journal of Topology and Analysis, Reviews in Mathematical Physics, and Proceedings of the American Mathematical Society Series B.

Alan L. Carey was awarded the title of Fellow of the Australian Academy of Science in 2014.

Best Publications

  • Twisted K-theory and K-Theory of Bundle Gerbes

    Peter Bouwknegt;Alan L. Carey;Varghese Mathai;Michael K. Murray

  • UNBOUNDED FREDHOLM MODULES AND SPECTRAL FLOW

    Alan L. Carey;John Phillips

  • On fermion gauge groups, current algebras and Kac-Moody algebras

    A. L. Carey;S. N. M. Ruijsenaars

  • Spectral flow and Dixmier traces

    Alan Carey;John Phillips;Fedor A Sukochev

  • Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories

    Alan L. Carey;Stuart Johnson;Michael K. Murray;Danny Stevenson

  • The local index formula in semifinite Von Neumann algebras I: Spectral flow

    Alan Carey;John Phillips;Adam Charles Rennie;Fedor A Sukochev

  • Holonomy on D-branes

    Alan L. Carey;Stuart Johnson;Michael K. Murray

  • Operator Integrals, Spectral Shift, and Spectral Flow

    N A Azamov;Alan Carey;Peter Dodds;Fedor A Sukochev

  • Spectral flow in Fredholm modules, eta invariants and the JLO cocycle

    Alan L. Carey;John Phillips

  • Quantum Hall Effect on the Hyperbolic Plane

    Alan L. Carey;Keith Hannabuss;Varghese Mathai;P. J. McCann

  • The local index formula in semifinite von Neumann algebras II: the even case

    Alan Carey;John Phillips;Adam Charles Rennie;Fedor A Sukochev

  • INDEX THEORY, GERBES, AND HAMILTONIAN QUANTIZATION

    Alan L. Carey;Michael K. Murray;Jouko Mickelsson

  • A noncommutative framework for topological insulators

    Chris Bourne;Alan L. Carey;Adam Rennie

  • Index Theory for Locally Compact Noncommutative Geometries

    Alan Carey;V. Gayral;Adam Rennie;Fedor A Sukochev

  • General Existence Theorems for Orthonormal Wavelets, an Abstract Approach

    Larry Baggett;Alan L. Carey;William Moran;Peter Ohring

  • Automorphisms of the Canonical Anticommutation Relations and Index Theory

    Alan L. Carey;Charles Angas Hurst;D.M. O'Brien

  • The Dixmier trace and asymptotics of zeta functions

    Alan Carey;Adam Charles Rennie;Aleksandr Sedaev;Fedor A Sukochev

  • The Hochschild class of the Chern character for semifinite spectral triples

    Alan Carey;John Phillips;Adam Charles Rennie;Fedor A Sukochev

  • Quantum Hall Effect on the Hyperbolic Plane

    A. Carey;K. Hannabus;V. Mathai;P. McCann

  • Thom isomorphism and push-forward map in twisted K-theory

    Alan L. Carey;Bai-Ling Wang

  • BUNDLE GERBES APPLIED TO QUANTUM FIELD THEORY

    Alan L. Carey;Jouko Mickelsson;Michael K. Murray

Frequent Co-Authors

Fedor Sukochev
Fedor Sukochev University of New South Wales
Fritz Gesztesy
Fritz Gesztesy Baylor University
Varghese Mathai
Varghese Mathai University of Adelaide
Harald Grosse
Harald Grosse University of Vienna
Matilde Marcolli
Matilde Marcolli California Institute of Technology
Thierry Coulhon
Thierry Coulhon PSL University
Ruibin Zhang
Ruibin Zhang University of Sydney
Ole E. Barndorff-Nielsen
Ole E. Barndorff-Nielsen Aarhus University
Michael Cowling
Michael Cowling University of New South Wales
Peter G. Taylor
Peter G. Taylor University of Melbourne

If you think any of the details on this page are incorrect, let us know.

Report an issue

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Related Online Degrees & Career Pathways

For students interested in Mathematics, exploring related online degrees can open diverse career opportunities. A strong foundation in analytical skills makes programs like analytics masters programs highly relevant. These programs build on mathematical principles to equip graduates with expertise in data-driven decision-making, a skill in high demand across industries.

Many professionals also consider business education to complement their math skills. If you’re looking for flexible options, it's worth exploring the range of easiest mba specialization programs, designed to provide practical business knowledge without overwhelming entry requirements.

Additionally, the convenience of remote learning has boosted the popularity of the easiest online mba. These programs offer the chance to advance your career alongside current commitments, making them ideal for those seeking leadership roles without a traditional campus experience.

For those aiming at top-tier management positions or entrepreneurial ventures, online dba programs provide advanced research and business strategy knowledge, blending theory with practical applications. Together, these related online degrees can significantly enhance mathematical careers by broadening skill sets and expanding professional possibilities.

Best Scientists Citing Alan L. Carey

Trending Scientists

Recently Published Articles