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Durham University

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Staff Profile

John Hunton, PhD University of Cambridge

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Deputy Head of Department, Professor, Topology in the Department of Mathematical Sciences

Contact John Hunton

Research Groups

Department of Mathematical Sciences

  • Pure Mathematics
  • Pure Mathematics: Topology

Research Interests

  • Algebraic Topology
  • Aperiodic Tilings
  • Topological Dynamics


Chapter in book

Journal Article

  • Hunton, J R & Walton, J J (Accepted). Aperiodicity, rotational tiling spaces and topological space groups. Advances in Mathematics
  • Alvarez Lopez, Jesus A, Barral Lijo, Ramon, Hunton, John, Nozawa, Hiraku & Parker, John R (Accepted). Chaotic Delone Sets. Discrete and Continuous Dynamical Systems
  • Clark, Alex & Hunton, John (2019). The homology core of matchbox manifolds and invariant measures. Transactions of the American Mathematical Society 371(3): 1771-1793.
  • Hunton, J, Gähler, F & Kellendonk, J (2013). Integral cohomology of rational projection method patterns. Algebraic & Geometric Topology 13(3): 1661-1708.
  • Hunton, J & Clark, A (2012). Tiling spaces, codimension one attractors and shape. New York Journal of Mathematics 18: 765-796.
  • Hunton, J, Barge, M, Diamond, B & Sadun, L (2010). Cohomology of substitution tiling spaces. Ergodic Theory and Dynamical Systems 30(06): 1607-1627.
  • Hunton, J, Green, EL & Snashall, N (2008). Coverings, the graded centre and Hochschild cohomology. Journal of Pure and Applied Algebra 212(12): 2691–2706.
  • Gähler, Franz, Hunton, John R. & Kellendonk, Johannes (2008). Integer Cech cohomology of icosahedral projection tilings. Zeitschrift für Kristallographie 223(11-12).
  • Hunton, John & Shchukin, Mikhail (2006). The K-Theory of C*-Algebras with Finite Dimensional Irreducible Representations. Integral Equations and Operator Theory 54(1): 89.
  • Hunton, J.R. & Schuster, B. (2005). Subalgebras of group cohomology defined by infinite loop spaces. Topology 44(4): 689.
  • Bendersky, Martin & Hunton, John R. (2004). ON THE COALGEBRAIC RING AND BOUSFIELD–KAN SPECTRAL SEQUENCE FOR A LANDWEBER EXACT SPECTRUM. Proceedings of the Edinburgh Mathematical Society 47(3): 513.
  • Green, D.J., Hunton, J.R. & Schuster, B. (2003). Chromatic characteristic classes in ordinary group cohomology. Topology 42(1): 243.
  • Forrest, A, Hunton, J & Kellendonk, J (2002). Cohomology of canonical projection tilings. Communications in Mathematical Physics 226: 289-322.
  • Hunton, J R (2002). Complete cohomology theories and the homology of their omega spectra. Topology 41: 931-943.
  • Forrest, A, Hunton, J & Kellendonk, J (2002). Topological Invariants for Projection Method Patterns. Memoirs of the American Mathematical Society 159(758): i-x, 1-120.
  • Clarke, F, Hunton, J & Ray, N (2001). Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems. Annalesde l' Institut Fourier 51: 297-336.
  • Forrest, A & Hunton, J (1999). The cohomology and K-theory of commuting homeomorphisms of the Cantor set. Ergodic Theory and Dynamical Systems 19: 611-625.
  • Hunton, J R & Turner, P R (1999). The homology of spaces representing exact pairs of homotopy functors. Topology 38(3): 621-634.
  • Hunton, J R & Turner, P R (1998). Coalgebraic algebra. Journal of Pure and Applied Algebra 129: 297-313.
  • Hunton, J, Mimura, M, Nishimoto, T & Schuster, B (1998). Higher v_n torsion in Lie groups. Journal of the Mathematical Society of Japan 50(4): 801-818.
  • Hunton, J (1998). The complex oriented cohomology of extended powers. Annales de l'Institut Fourier 48(2): 517-534.
  • Hunton, J & Ray, N (1995). A rational approach to Hopf rings. Journal of Pure and Applied Algebra 101: 313-333.
  • Hopkins, M J & Hunton, J R (1995). On the structure of spaces representing a Landweber exact cohomology theory. Topology 34(1): 29-36.
  • Hunton, J (1995). The Boardman homomorphism. Contemporary Mathematics 181: 251-262.
  • Baker, A & Hunton, J (1994). Continuous Morava K-theory and the geometry of the I_n-adic tower. Mathematica Scandinavica 75: 67-81.
  • Hunton, J (1992). Detruncating Morava K-theory. London Mathematical Society Lecture Note Series 176: 35-43.
  • Hunton, J (1990). The Morava K-theories of wreath products. Mathematical Proceedings of the Cambridge Philosophical Society 107: 309-318.

Conference Paper

  • Hunton, John (2017), Topological Invariants for Tilings, in Baake, Michael, Damanik, David, Kellendonk, Johannes & Lenz, Daniel eds, 14: Spectral Structures and Topological Methods in Mathematical Quasicrystals. Oberwolfach, Germany, European Mathematical Society, 2814-2817.
  • Forrest, A, Hunton, J & Kellendok, J (2001), Cohomology groups for projection point patterns, XIII International Congress of Mathematical Physics. London, 333-339.

Indicators of Esteem

    • Member, UKRI Future Leaders Fellowships Peer Review College
    • Member, EPSRC College, since 1999
    • Member, EPSRC Mathematical Sciences Strategic Advisory Team, 2010-2013
    • Chair and or member, EPSRC Fellowship, Programme, Doctoral Training and Standard Grant prioritisation panels, 2003, 2006, 2008, 2009, 2010, 2015, 2016, 2017, 2018
    • Trustee, London Mathematical Society, since 2011
    • Publications Officer, London Mathematical Soceity, since 2013
    • External Examiner (research degrees) Oxford, Lyon, Manchester, Sheffield, Leicester, Glasgow, Rabat, Southampton, Wuppertal
    • External Examiner (taught degrees) Manchester Unviersity (2002-6), Swansea Universlty (2006-11), Sheffield Universtiy (2012-16), Heriot-Watt University (2015- )
    • Chair, British Mathematical Colloquium 2011
    • Member, National Scientific Steering Committee, British Mathematical Colloquia 2008-17
    • Witness contributing to Burgess report on RCUK Open Access policy, 2014
    • Member, scientific advisory board for Deloitte’s work The Economic Benefits of Mathematical Sciences Research in the UK

    Since 2013 I have managed the Journals and Book Series published by the main UK Learned Society for Mathematics, the London Mathematical Society (LMS). These include

    • Proceedings, Journal, Bulletin and Transactions of the London Mathematical Society
    • The Journal of Topology
    • Compositio Mathematica (published on behalf of the Compositio Foundation)
    • Nonlinearity (published jointly with the Institute of Physics)
    • Mathematika (published on behalf of its owners, UCL)
    • Transactions of the Moscow Mathematical Soceity (English translation, published jointly with the Moscow Mathematical Society and the American Mathematical Society)
    • Izvestiya, Sbornik and Russian Mathematical Surveys (English translation, published jointly with the Russian Academy of Sciences and Turpion)
    • LMS Lecture Notes in Mathematics
    • LMS Student Texts

    My work is to lead on setting the publishing strategy, management of the contracts, oversight and appointment of editorial boards, and liaison with the publishing partners, including the commercial partners CUP, Wiley and IOPP with whom the Society contracts production, distribution and marketing.

    The Journals and Book Series operation of the LMS has a turnover of c.£2M per annum and all proceeds go to the charity. Like many UK Learned Societies, the income from these publications is critical to the funding of the Society, and underpins the grants it awards to Mathemticians. Publications funding also contributes to, amongst others, the running of Society meetings, the Popular Lectures, and policy work to engage with Government regarding mathematics education and funding for the mathematics people pipeline, in particular for mathematics research.


    Selected presenter, Royal Society Summer Science Exhibition 2009

    Selected presenter, EPSRC How? exhibition 2010

    Contributor Numberphile YouTube channel

    Plenary speaker, Trinity Mathematical Society Centenary Symposium, 2019

    • Panel chair at round table discussion on Mathematics Publishing for ECR’s at the 7th European Congress of Mathematics, Berlin 2016.

    • Plenary lecturer Dynamical Systems for Aperiodicity January 2016, Université Claude Bernard Lyon 1, Lyon, France.

    • Invited series of lectures, 31st Summer Conference on Topology and its Applications, hosted August 2016 by University of Leicester.

    • Plenary lecturer Topology and Dynamics conference, Leverhulme network, University of Leicester January 2017.

    • Plenary speaker, Oberwolfach workshop Spectral Structures and Topological Methods in Mathematical October 2017

    • Plenary speaker, Model Sets and Aperiodic Order, Durham, September 2018.

    • Plenary lecturer, 6 hours at Winter School on Tilings and Foliations, Santiago do Compostela, February 2019.

    • Invited Speaker, Annual Meeting of the Chinese Mathematical Society, Guangzhou, November 2019.