University of Auckland: Mathematics Department

Recent research highlights in the Department

This page lists a few examples of noteworthy research activity in the Mathematics department at the University of Auckland, under a number of headings:

New appointments

  • Dr Hannah Bartholomew to a Lectureship, with research interests in mathematics education

  • Dr Sina Greenwood to a Lectureship, with research interests in set-theoretic topology, nonmetrisable manifolds and reflection theorems in topology

  • Dr Mike Meylan to a Lectureship, with research interests in mathematical modelling and numerical techniques

  • Dr Warren Moors to a Lectureship, with research interests in Banach spaces, topology and set-valued analysis

  • Prof. Jozef Siran to an Associate Professorship, with research interests in algebraic and topological graph theory

  • Dr Shixiao Wang to a Lectureship, with research interests in nonlinear partial differential equations, fluid dynamics and industrial mathematics

    Notable research projects

  • Jianbei An and Charles Eaton (Birmingham) have classified up to Morita equivalence all blocks of finite groups having TI defect groups, and hence verified both Uno's projective conjecture and Dade's projective conjecture for blocks with TI defect groups.

  • Bill Barton is involved in a Mathematics Enhancement Project designed to enhance the participation and achievement of senior secondary mathematics students in low decile secondary schools; the project has just completed its first year of operation, with support from the Woolf Fisher Centre

  • Paul Bonnington, Dan Archdeacon and Jo Ellis-Monaghan (Vermont) have recently shown that all triangulations of the torus can be realised as 1-skeletons of (nonconvex) polyhedra in 3-space providing an extension of Steinitz' Theorem: 3-connected planar graphs can be realised as the 1-skeletons of convex polyhedra in 3-space; this work on the triangulations of the torus answers an important question from the 1970's posed by Branko Grunbaum

  • John Butcher has made good prgress on verifying the Butcher-Chipman conjecture, which is a claim (well-supported by numerical evidence) that the (now proved) Ehle conjecture extends to multivalue methods; this conjecture states that a generalized Pade approximation to the exponential function, with leading degree k and order p, cannot correspond to an A-stable numerical method if 2k-p > 2, and John has established the truth of the conjecture in some quadratic cases (applicable to two-step numerical methods)

  • Bruce Calvert has extended the 1970s work of Desoer and Wu on nonlinear monotone networks

  • Marston Conder and Arkadii Slinko have refuted a conjecture by Fishburn on comparative probability orderings on finite sets

  • Rod Gover is doing joint work with Tom Branson (University of Iowa) on a number of topics including: construction of a huge class of non-standard conformally invariant operators on differential forms, a conformally invariant Hodge theory for even-dimensional conformal manifolds, and conformally invariant operators between low and high de Rham cohomology spaces on even dimensional manifolds

  • Gaven Martin has announced the solutions of a number of problems including identification of the minimal co-volume lattice acting on hyperbolic 3-space (thereby identifying 3-manifolds with optimal automorphism group), the identification of all the two generator arithmetic Kleinian groups generated by torsion of order >= 6 (with Colin Maclachlan), and a partial solution of the Lichnerowicz problem to identify those manifolds admitting rational automorphisms (joint work with with V. Mayer, solving the problem in the case n = 3, and giving topological conditions such as growth rates of fundamental groups for the case n >= 4)

  • Geoff Nicholls is engaged in joint work with Russell Gray (Psychology) to put a date on Indo-European, the ancestral language for a diverse collection of languages including such apparently unrelated languages as Afghan, Albanian, Portuguese, English and Swedish; their work depends on an analysis of a branching process model of language evolution (using ideas from percolation theory and the analysis of physical critical phenomena), and their preliminary results were reported on the National station's radio program "Eureka"

    Major research grants or awards

  • Marsden Fund grant (2003) to Paul Bonnington and Jozef Siran

  • Marsden Fund grant (2003) to John Butcher and Allison Heard

  • Marsden Fund grant (2003) to D. Brunton, H. Ross, Geoff Nicholls, R. Gray and A. Rodrigo

  • Marsden Fund grant (2003) to V. Squire, Mike Meylan, D. Evans, R. Porter and S. Sakai

  • Ministry of Education grant (2003) to Bill Barton and Pip Neville-Barton

  • Ministry of Education grant (2003) to Bill Barton and Hannah Bartholomew

  • NZIMA Programme funding (2004) to Vivien Kirk, M. McGuinness, R. McLachlan, R. Murray and R. Quispel

  • NZIMA Programme funding (2004/05) to Paul Bonnington and Geoff Whittle

  • NZIMA Programme funding (2005) to Gaven Martin and Eamonn O'Brien

  • JSPS Fellowship (2003) to Boris Pavlov

  • Ambassade de France en Nouvelle-Zelande Service Culturel grant (2003) to David Gauld

  • NZ Science & Technology Postdoctoral Fellowship (2002) to Mark Harmer

  • NZ Science & Technology Postdoctoral Fellowship (2003) to Richard Evans

  • Award of NZ$1,835,000pa from the NZ government's Centres of Research Excellence Fund to support the newly-established NZ Institute of Mathematics and its Applications (Directors: Marston Conder and Vaughan Jones; also John Butcher, David Gauld and Gaven Martin were involved in this, one of five successful proposals in March 2002)

  • Marsden Fund grant (2002) to Rod Gover

  • Fast Start Marsden Fund grant (2002) to Shayne Waldron

  • Miller (Visiting) Research Professorship, University of California Berkeley, to Gaven Martin (for one month September/October 2002)

  • Vice-Chancellor's University Development Fund award (2002) to Boris Pavlov and colleagues in Physics and Computer Science for further investigations in the field of quantum computing

  • RSNZ James Cook Fellowship (2001-04) to Gaven Martin

  • Marsden Fund grant (2001) to Bill Barton and Ivan Reilly

  • Marsden Fund grant (2001) to Marston Conder, Jianbei An and Eamonn O'Brien

  • Marsden Fund grant (2001) to Russell Gray (Psychology) and Geoff Nicholls

  • Marsden Fund grant (2001) to Vaughan Jones, Marston Conder, Rod Downey and Gaven Martin

  • Marsden Fund grant (2001) to Gaven Martin

  • Vice-Chancellor's University Development Fund award (2001) to Allen Rodrigo, John Taylor and Geoff Nicholls to develop a mathematical model of the epidemic of the Feline Immuno-deficiency Virus (FIV)

    Invitations to international conferences

  • Bill Barton to the 3rd European Conference on Research in Mathematics Education (CERME-3), Bellaria, Italy (February 2003), the Midsummer World Mathematics Education conference, Goteborg, Sweden (June 2003), and the Saami Conference on Ethnomathematics, Jukkasjärvi, Sweden (June 2003)

  • John Butcher to SciCADE 2003, Trondheim, Norway (30 June-4 July 2003), Advances and Challenges in Time-Integration of PDEs, Providence RI, USA (August 2003), NumDiff 2003, Halle, Germany (September 2003), ICCMSE 2003, Kastoria, Greece (September 2003)

  • Marston Conder to Conference on Groups and Computation, Columbus, Ohio (March 2003), Conference on Algebraic Combinatorics, Koper, Slovenia (June 2003) and Conformal Geometry, Discrete Groups and Surfaces, Bedlewo, Poland (June/July 2003)

  • Rod Gover to Conference on Conformal structure in Geometry, Analysis and Physics, Palo Alto, California (2003)

  • Chris King to "Quantum Mind 2003", Arizona (March 2003)

  • Vivien Kirk to Workshop on Pattern Formation, Colorado (May 2003) and SIAM Meeting on Applications of Dynamical Systems (May 2003)

  • Norm Levenberg to Nordan Several Complex Variables, Sweden (May 2003) and International Meeting in Approximation Theory, Tennessee (May 2003)

  • Gaven Martin to Tri-nations Conference on Geometric Aspects of Analysis, Batemans Bay, Australia (February 2003), Miller Conference in the Basic Sciences, Berkeley, California (June 2003), Nevanlinna Colloquium, Jyvaskyla, Finland (June 2003)

  • Mike Meylan to ISOPE Conference, Hawaii (May 2003)

  • Geoff Nicholls to 18th International Radiocarbon Conference, Wellington (September 2003) and Conference on Mathematics and Statistics of Complex Systems, Melbourne (November 2003)

  • Eamonn O'Brien to Conference on Groups and Computation, Columbus, Ohio (March 2003) and International Workshop on Representation Theory, Canberra (June 2003)

  • Judy Paterson to Mathematics Education Conference "Around the World: Bridging Policy and Practice: A Focus on Teacher Preparation", Utah (July 2003)

  • Maxine Pfannkuch to ISI-54 Conference and IASE Satellite Conference, Berlin (August 2003)

  • Ivan Reilly to Coker Memorial Conference Haceteppe University, Ankara, Turkey (April 2003)

  • Philip Sharp to the Annual conference for the American Astronomical Society's division on Dynamical Astronomy, Cornell University (May 2003)

  • Arkadii Slinko to International Symposium on Control Sciences, Moscow (June 2003)

  • Mike Thomas to 27th Conference of the International Group for the Psychology of Mathematics Education, Honolulu, Hawaii (July 2003)

  • Shayne Waldron to Conference on Advances in Constructive Approximation, Tennessee (May 2003), Workshop on Constructive Mathematics (honouring Carl de Boor), Schloss Dagstuhl, Germany (June 2003), and Workshop on time-frequency analysis and applications, Singapore (September 2003)

  • In addition, several members of the Department helped organise and participated in the large international conference on undergraduate education, Remarkable Delta'03 (DELTA), held at Queenstown (November 2003)

    Selected recent research publications

    ALI, M.M., SMITH, D.J.: 'Generalized GCD Rings II'. Beiträge zur Algebra und Geometrie, 44 (1), 75-98, 2003.

    AMBRUSTER, D., STONE, E., KIRK, V.: 'Noisy heteroclinic networks'. Chaos, 13, 71-79, 2003.

    AN, J., O'BRIEN, E.A., WILSON, R.A.: 'The Alperin weight conjecture and Dade's conjecture for the finite simple groups J_4'. London Mathematical. Society Journal of Computation and Mathematics, 6, 119-140, 2003.

    AN, J., O'BRIEN, E.A.: 'Conjectures on the character degrees of the Harada-Norton simple group HN'. Israel Journal of Mathematics, 137, 157-182, 2003.

    ARCHDEACON, D., BONNINGTON, C.P., DEBOWSKI, M., PRESTIDGE, M.: 'Halin's theorem for the Moebius strip'. Ars Combinatoria, 68, 243-256, 2003.

    BARTHOLOMEW, H., RODD, M.: 'A firecely held modesty: the experiences of women studying mathematics'. In: M.O.J. Thomas and G. Oates (Eds), New Zealand Journal of Mathematics, 32 (Supplementary Issue), 9-18, 2003.

    BARTON, B., NEVILLE-BARTON, P.: 'Language Issues in Undergraduate Mathematics: A Report of Two Studies'. New Zealand Journal of Mathematics, 32 (Supplementary Issue), 19-28, 2003.

    BLAOM, A.D.: 'Reconstruction phases for cotangent bundles'. Documenta Mathematica, 7, 561-604, 2002.

    BLOOM, T., LEVENBERG, N.: 'Weighted pluripotential theory in C^n'. American Journal of Mathematics 125(1), 57-103, 2003.

    BLOOM, T., LEVENBERG, N., MA'U, S.: 'Robin functions and extremal functions'. Annales Polonici Mathematici, 80, 55-84, 2003.

    BLOOM, T., LEVENBERG, N.: 'Distribution of nodes on algebraic curves in C^n'. Annales de l'Institut Fourier, 53(5), 1-21, 2003.

    BONNINGTON, C. P., RICHTER, R.: 'Bruce Graphs embedded in the plane with a bounded number of accumulation points'. Journal of Graph Theory, 44 (2), 132-147, 2003.

    BONNINGTON, C. P., KLAVZAR, S., LIPOVEC, A.: 'On cubic and edge-critical isometric subgraphs of hypercubes'. AustralasianJournal of Combinarorics, 28, 217-224, 2003.

    BONNINGTON, C.P., WATKINS, M.E.: 'Planar embeddings with infinite faces'. Journal of Graph Theory, 42(4), 257-275, 2003.

    BOS, L., BRUDNYI, A., LEVENBERG, N., TOTIK, V.: 'Tangential Markov inequalities on transcendental curves'. Constructive Approximation, 19, 339-354, 2003.

    BOS, L., WARE, A., PAVLOV, B.: 'On semi-spectral method for pricing an option on a mean-reverting asset'. Quant. Finance, 5, 337-345, 2002.

    BUJALANCE, E., CIRRE, E., CONDER, M. D. E.: 'On extendability of group actions on compact Riemann surfaces'. Transactions of the American Mathematical Society, 355, 1537­1557, 2003.

    BUTCHER , J. C., Numerical Methods for Ordinary Differential Equations, J. Wiley, Chichester, 439 pp., 2003.

    BUTCHER, J. C., JACKIEWICZ, Z.: 'A new approach to error estimation for general linear methods'. Numerische Mathematik, 95, 487-502, 2003.

    BUTCHER, J.C., MOIR, N.: 'Experiments with a new fifth order method'. Numerical Algorithms, 3, 137-151, 2003.

    BUTCHER, J. C., WRIGHT, W. M.: 'A transformation relating explicit and diagonally-implicit general linear methods', Applied Numerical Mathematics, 44, 313-327, 2003.

    CALVERT, B.: 'Monotone multierminal resistors and large networks'. Memoirs of the Faculty of Science and Engineering, Shimane University, 36, 21-38, 2003.

    CAO, J., GANSTER, M., KONSTADILAKI, C., REILLY, I.: 'On preclosed sets and their generalizations'. Houston Journal of Mathematics, 28, 771-780, 2002.

    CAO, J., REILLY, I., XIONG, H.: 'A lattice-valued Banach-Stone theorem'. Acta Mathematica Hungarica, 98 103-110, 2003.

    CAO, J., SONG, Y.: 'Aquaro-number versus star-Lindelof number'. Houston Journal of Mathematics, 29, 925-936, 2003.

    CONDER, M.D.E., MACLACHLAN, C., TODOROVIC VASILJEVIC, S., WILSON, S.: 'Bounds for the number of automorphisms of a compact non-orientable surface'. Journal of the London Mathematical Society, 68, 65­82, 2003.

    CONDER, M. D. E., MARUSIC, D. 4: 'A tetravalent half-arc-transitive graph with nonabelian vertex stabilizer'. Journal of Combinatorial Theory Series B, 88, 67­76, 2003.

    CONDER, M. D. E., MORTON, M.J.1 , PRAEGER, C.E.: 'Two-arc closed subsets of graphs'. Journal of Graph Theory, 42, 350­364, 2003.

    DELOS SANTOS, A.G., THOMAS, M.O.J.: 'Perspectives on the teaching of derivative with graphic calculators'. Australian Senior Mathematics Journal, 17(1), 40-58, 2003.

    DRUMMOND, A.J., NICHOLLS, G.K., RODRIGO, A.G. 2 , SOLOMON, W.: 'Genealogies from time-stamped sequence data'. In: Buck, C. and Millard, A. (ed.), 'Tools for Constructing Chronologies', Springer, pp.151-174, 2003.

    FOX, C., NICHOLLS G.K.: 'Statistical Estimation of the Parameters of a PDE'. Canadian Applied Mathematics Quarterly, 10(2), 277-306, 2002.

    GARTSIDE, P.M., GLYN, A., MCINTYRE, D.W.: 'Relative Calibers'. Topology and its Applications, 132, 203­219, 2003.

    GEHRING, R.W., MARSHALL, T.H., MARTIN, G.J.: 'Recent results in the geometry of Kleinian groups'. Computational Methods and Function Theory, 2(1), 249-256, 2003.

    GREENWOOD, S.: 'Constructing Type I nonmetrisable manifolds with given Y-trees'. Topology and its Applications, 123, 91-101, 2003.

    HAFNER, P.R.: 'The Hoffman-Singleton graph and its automorphisms'. Journal of Algebraic Graph Theory, 18, 7-12, 2003.

    IWANIEC, T., KOSKELA, P., MARTIN, G., SBORDONE, C.: 'Mappings of finite distortion: L^n log x L-integrability'. Journal of the London Mathematical Society (2), 67(1), 123-136, 2003.

    JONES, M., NICHOLLS, G.K.: 'New Radiocarbon Calibration Software', Radiocarbon, 44(3), 663-674, 2002.

    MARINOV, C., CALVERT, B.: 'Performance analysis for a k-winner-take-all anolog neural network: basic theory'. IEEE Transactions on Neural Network, 14, 766-780, 2003.

    MARSHALL, T.H., MARTIN, G.J.: 'Packing strips in the hyperbolic plane'. Proceedings of the Edinburgh Mathematical Society (2), 46(1), 67-73, 2003.

    MARSHALL, T.H., MARTIN, G.J.: 'Volumes of hyperbolic 3-manifolds'. Notes on a paper of D. Gabai, G. Meyerhoff and P. Milley, 'Volumes of tubes in hyperbolic 3-manifolds', Conformal Geometry and Dynamics, 7, 34-48, 2003.

    MARTIN, G.J., MAYER, V.: 'Rigidity in holomorphic and quasiregular dynamics'. Transactions of the American Mathematical Society, 355(11), 4349-4363, 2003.

    MEYLAN, M.H., GROSZ, L.: 'A parallel algorithm to find the zeros of a complex analytic function'. ANZIAM Journal, 44(E), E216-E234, 2003.

    MOORS W.B., SOMASUNDARAM S.: A weakly Stegall space that is not a Stegall space, Proceedings of the American Mathematical Society, 131, 647-654, 2003.

    NIEDERER, K., IRWIN, R.J., IRWIN, K.C., REILLY, I.: 'Identification of mathematically gifted children in New Zealand', High Ability Studies, 14, 71-84, 2003.

    PFANNKUCH, M., PARSONAGE, R., and REGAN, M.: 'Statistical literacy: How should we teach it to large introductory statistics courses?'. New Zealand Journal of Mathematics, 32 (Supplementary Issue), 145­154, 2003.

    SLINKO, A.: 'Majoritarian Compromise in Large Societies'. Review of Economic Design, 7(3), 343-350, 2002.

    STEWART, S., THOMAS, M.O.J.: 'Difficulties in the acquisition of linear algebra concepts'. New Zealand Journal of Mathematics, 32, 207-215, 2003.

    STRATTON, W., REILLY,I.: 'An undergraduate course for talented high school students'. In: B. Barton, G. Oates, I. Reilly and M. Thomas (eds), Communications of Remarkable Delta03, Fourth Southern Hemisphere Symposium on Undergraduate Mathematics and Statistics Teaching and Learning, Queenstown, New Zealand, November 2003, International Delta Steering Committee, 247- 251, 2003.

    TAYLOR, S.W., YAU, S.: 'Boundary Control of a Rotating Timoshenko Beam'. ANZIAM Journal, 44 (E), 143-184, 2003.

    TEE, G.J.: 'Russian peasant multiplication and Egyptian division in Zeckendorf arithrimetic'. Australian Mathematical Society Gazette 30(5), 267-276, 2003.

    THOMAS, M.O.J., HOLTON, D.: 'Technology as a Tool for Teaching Undergraduate Mathematics'. In: A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F.K.S. Leung (ed.) Second International Handbook of Mathematics Education, vol.1, Dordrecht, Kluwer, 347-390, 2003.

    WALDRON, S.: 'A generalised beta integral and the limit of the Bernstein-Durrmeyer operator with Jacobi weights', Journal of Approximation Theory 122( 1), 141-150, 2003.

    WALDRON, S.: 'Generalised Welch Bound Equality sequences are tight frames', IEEE Transactions on Information Theory 49( 9), 2307-2309, 2003.

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    Last updated: 9 March 2004