This is the second in a series of news bulletins concerning activities of staff and students and visitors in the Mathematics Department at the University of Auckland. The first bulletin was published in April 1996 and copies are available from the Department Office (SMIS/Physics building, 38 Princes St, Auckland, Tel. (09) 373-7599 ext. 8743, FAX (09) 373-7457).
This bulletin and the first one can also be read from the Department's WWW home page, at: http://www.math.auckland.ac.nz/
"for his prolific and far-reaching work in analysis and topology, especially for his contributions to the theory of quasiconformal mappings and special functions -- contributions that are characterized by both analytic ingenuity and geometric insight".
These awards were initiated in 1990 to foster and promote mathematical research in New Zealand and to recognise the research achievements of N.Z. mathematicians. This is the fourth award to a member of the Mathematics Department at the University of Auckland, with previous award winners including Professors John Butcher (1991), Marston Conder (1993) and Gaven Martin (1994).
In 1995 Paul and his former PhD supervisor Charles Little published The Foundations of Topological Graph Theory. This book begins with a graph-theoretic proof of the classification of topological surfaces and a generalisation of the Jordan curve theorem, and then goes on using the novel approach of 3-graphs to develop the foundations of the subject further. It has just earned a very positive review in Zentralblatt fuer Mathematik:
"This manuscript excellently complements the existing books of Gross & Tucker and White. The authors succeed in their main goal of placing topological graph theory on a purely combinatorial yet rigorous footing. The combination of this success and the writing style make this an excellent book. It is strongly recommended to both the prentice and practitioner of this fascinating field."
During the past three years, Paul has enjoyed a fruitful collaboration with several others in this field including Dan Archdeacon (Vermont), Charles Little (Massey), Jozef Siran (Bratislava) and Bruce Richter (Ottawa), and is now working with his PhD student John Pearson on a computer-assisted search for minimal obstructions to embedding a graph on a torus.
Geoff has been working on enhancing automatic intermediate level image pattern extraction, which amounts to specifying a normalisable measure on a space of image patterns, and devising an algorithm to sample this measure. Most recently his work has concentrated on optimising an implementation of the sampling algorithm (a computer program), and enlarging the space of states so that the grey level as well as the edge structures are treated as random variables. There has been quite a lot of interest in a preprint of one of his papers describing this work, with Department web statistics showing that several copies are being downloaded each week.
In another area Geoff has been working to improve a result he achieved last year about phase transition in a continuum model of a magnet. He has been invited to give a number of seminar talks on this subject: "Spontaneous magnetisation in the plane".
In recent years Vaman has been an active contributor to a successful collaboration involving co-authors from four different continents: Anderson, Aseev, Qiu, Vamanamurthy and Vuorinen (or AAQVV). In particular the book Conformal Invariants, Inequalities and Quasiconformal Maps by Glen Anderson, Vamanamurthy and Matti Vuorinen has just been accepted for publication by Wiley.
Also Vaman acted as Head of the Mathematics Department from August 1994 to December 1995.
Graeme is involved in a number of modelling projects with industrial clients and research institutes. Currently these include deterministic and stochastic dynamical systems models of agricultural processes (pasture fertiliser systems, soil sustainability, carcass composition), ecological projects (predation of kiwis) and chemical engineering (theory of thermal ignition). These invariably involve the use and further development of advanced techniques in non-linear partial differential equations.
Graeme currently supervises or co-supervises no fewer than five PhD students, is sub-contracted on several PGSF projects by AgResearch, and has recently forged a contract with Fisher & Paykel on the dynamics of washing machines. He will be an invited contributor to the forthcoming programme on mathematical modelling of plankton population dynamics at the Isaac Newton Institute in Cambridge (U.K.) in August. Also Graeme is convenor of the Royal Society of New Zealand's standing committee on mathematical and information sciences, and chair of the Australia and New Zealand Industrial and Applied Mathematics group (ANZIAM) until February 1997.
The Department now has 27 PhD students, following the registration of Tsukasa Yashiro for a PhD in "Immersions in Manifolds" with supervisor Gaven Martin and adviser Tim Marshall. There has been an increase of 150 doctoral students at the University of Auckland in the three years 1993-95, during which the School of Mathematical and Information Sciences has seen its PhD student numbers rise from 10 to 53 (representing more than 25% of the total University increase).
The following were also successful in the April round of grants from the Auckland University Research Committee:
Jianbei An attended the International Group Theory Symposium in Beijing in May, and established contact with several mathematicians in China (at the Capital Normal University, Peking University and Nanjing University), who will work with him on projects related to Alperin's and Dade's conjectures for various finite simple groups.
John Butcher has returned from study and research leave in South America, the U.S., Europe and Australia, and is taking up the position of Research Coordinator in the Department. He is also active as Editor of the N.Z. Journal of Mathematics, with assistance from Joel Schiff as Managing Editor.
Marston Conder has been appointed by the Ministry of Research, Science & Technology as a "lead expert" in the mathematical sciences to help coordinate the production of a profile of New Zealand's scientific knowledge base, and by the Foundation for Research, Science & Technology to its Advisory Committee for N.Z. Science & Technology Postdoctoral Fellowships. Also he will be an invited speaker at the conference on Geometric Group Theory in Canberra in July.
Colin Fox appeared in a screening of the final programme "Refining the View" in the Open University/BBC Education TV series "Seeing through Mathematics" in the Department in June. This 30-minute programme was made as part of the Open University's new foundation course in mathematical modelling, and has a large N.Z. component featuring interviews with Colin and including items on the construction of bamboo scaffolding in Hong Kong, monitoring the survival rate of the Hector's dolphin population, Antarctic sea-ice, and the fluctuation in the water-level of Lake Wakatipu. The first programme had an audience of over half a million when screened in the U.K. in February.
David Gauld has been serving as the University's Assistant Vice-Chancellor (Research) for most of the last two years. Recently he attended a conference on Quality in Postgraduate Education in Adelaide and a conference on Evaluation of Science in Wellington.
Vivien Kirk has returned from study and research leave in the U.S. and Canada, and has recently been elected to the Council of the NZ Mathematical Society.
Gaven Martin spent three weeks in Scandinavia at the end of the first semester. He gave an invited lecture at a conference on Conformal Geometry at Trondheim (Norway), and he and Norm Levenberg gave invited lectures at a meeting of the Swedish Mathematical Society at Umea (Sweden). He will also be an invited speaker at the conference on Geometric Group Theory in Canberra in July.
Warren Moors (N.Z. Science & Technology Postdoctoral Fellow) was recently a plenary speaker at the 25th Spring conference of the Union of Bulgarian Mathematicians, at Kazanlak, Bulgaria.
Margaret Morton has returned from study and research leave in the U.S., Canada and Australia, during which time she attended and gave talks at conferences in Beijing and Sydney.
Garry Tee is attending the Annual Meeting of the Australian Mathematical Society in Adelaide in July. He was recently asked to assist with an interesting piece of mathematical detective work: calculating the site of Charles Kingsford-Smith's fatal plane crash off the coast of Burma in 1934.
Wayne Walker has been working with Professor Q.I. Rahman from the University of Montreal, who visited the Department for a month to work with him on functions of exponential type. It is known that if these functions are bounded on the real axis then their rate of increase or decrease may be arbitrarily slow, which is contrary to the intuition of those who visualise these functions as signals. Visualisation of this kind does however give good information about how rapidly such a function can increase or decrease. Prof. Rahman and Dr Walker have been able to establish a connection between the notions of slow and fast. This is particularly interesting when the Fourier transform of the signal is a multi-band and in this case the mathematical results correspond better to intuition.
Mark Wilson (N.Z. Science & Technology Postdoctoral Fellow) has recently completed a multi-paper programme of applying Bell's criterion to simple finite-dimensional Lie superalgebras over an algebraically closed field of characteristic zero. As a consequence he has obtained many new prime rings, and also some insight into the representation theory of these algebras. He will talk on his work and establish links with European colleagues at the international Ring Theory conference (a satellite conference of the 2nd European Congress of Mathematicians) in Hungary in July.
This year's mathematics summer workshop will take place again at Tolaga Bay, from 3-11 January 1997, with the theme of discrete groups and hyperbolic manifolds, and supported by the Department and by grants from the Marsden Fund for basic research. Invited speakers include Martin Bridson (Oxford), David Epstein (Warwick), Andre Haefliger (Geneva), Linda Keen (CUNY, New York), Colin Maclachlan (Aberdeen), Walter Neumann (Melbourne) and David Singerman (Southampton).
A joint meeting of the Australian and New Zealand Mathematical Societies will be hosted by the University of Auckland the week 7-11 July 1997, and already an impressive list of invited speakers is in train. The Conference Director is Prof. Gaven Martin (martin@math.auckland.ac.nz).
Following the MERGA (Maths Education Research Group of Australasia) conference the same week in Rotorua, a meeting of the Bridging Maths Network of Australasia will be hosted by the Department's Mathematics Education Unit here in Auckland.
Jianbei An, Dade's conjecture for 2-blocks of symmetric groups, University of Auckland Mathematics Department Report Series, no.333, 1996.
G.D. Anderson, M.K. Vamanamurthy & M. Vuorinen, Conformal Invariants, Inequalities and Quasiconformal Maps (Wiley), in press.
Bill Barton, Anthropological Perspectives on Mathematics and Mathematics Education, in: The International Handbook on Mathematics Education (Alan Bishop ed.), in press.
Emilio Bujalance & Marston Conder, On cyclic groups of automorphisms of Riemann surfaces, University of Auckland Mathematics Department Report Series, no.336, 1996.
Jiling Cao, Answers to two questions of Papadopoulos, Questions and Answers in General Topology 14 (1996), 111-116.
R.P.K. Chan & P. Chartier, A composition law for Runge-Kutta methods applied to index-2 differential-algebraic equations, BIT 36 (1996), 229-246.
M.D.E. Conder, M.J. Morton & C.E. Praeger, Partition graphs for finite symmetric groups, University of Auckland Mathematics Department Report Series, no.337, 1996.
C. Fox, L. Wilcocks & T. Haskell, A calculation of sea-ice Young's modulus using under-ice pres-sure measurements, University of Auckland Mathematics Department Report Series, no.335, 1996.
J.R. Giles & W.B. Moors, Generic continuity of restricted weak upper semi-continuous set-valued mappings, Set Valued Analysis 4 (1996), 25-39.
J.R. Giles, P.S. Kenderov, W.B. Moors & S.D. Sciffer, Generic differentiability of convex functions on the dual of a Banach space, Pacific J. Mathematics 172 (1996), 413-433.
C. Good, D. McIntyre & W.S. Watson, Measurable cardinals and finite intervals between Hausdorff topologies, University of Auckland Mathematics Department Report Series, no.334, 1996.
P.S. Kenderov & W.B. Moors, Game characterisation of fragmentability of topological spaces, Proceedings of the 25th Spring conference of the Union of Bulgarian Mathematicians (Kazanlak, Bulgaria, 1996), pp.8-18.
A. McNabb, C. Gooch, A.K. van Zyl & G.C. Wake, A diffusion-reaction model for corrosion of zinc coated steel under polymer paint films, in: Differential Equations and Applications to Biology and to Industry (ed. M. Martelli et al), World Scientific, 1996, pp.355-368.
Warren B. Moors, A selection theorem for weak upper semi-continuous set-valued mappings, Bull. Australian Math. Society 53 (1996), 213-227.
S-L. Qiu and M. K. Vamanamurthy, Sharp estimates for complete elliptic integrals, SIAM Journal of Mathematical Analysis 27 (1996), 823-834.
S.D. Scott, On the finiteness and uniqueness of certain 2-tame N-groups, Proceedings of the Edinburgh Mathematical Society 38 (1995), 193-205.
S.D. Scott, On the structure of certain 2-tame near-rings, in: Near Rings and Near Fields (ed. Y. Fong et al), Kluwer Academic Publications, 1995, pp.239-256.
M. Suzuki, A. McNabb & A.J. Bracken, A boundary flux property for a general nonlinear diffusion reaction system, SIAM Special Issue in honour of Ivar Stakgold, 1996, pp.235-239.
Tuan Seng Chew, B. van Brunt & G.C. Wake, On retarded functional differential equations and Henstock-Kurzweil integrals, Differential and Integral Equations 9 (1996), 569-580.
G.C. Wake, K. Louie & M.G. Roberts, The regulation of an age-structured population by a fatal disease with or without dispersion, in: Differential Equations and Applications to Biology and to Industry (ed. M. Martelli et al), World Scientific, 1996, pp.553-562.
S.D. Watt & G.C. Wake, Uncertainty in epidemic models, in: Nonlinear Problems in Applied Mathematics, SIAM (Philadelphia), 1995, pp.250-258.
W.S.D. Wilcock & Alex McNabb, Estimates of crustal permeability on the Endeavour segment of the Juan de Fuca mid-ocean ridge, Earth and Planetary Letters 138 (1996), 83-91.
Mark C. Wilson, Primeness of the enveloping algebra of a Cartan type Lie superalgebra, Proceedings of the American Mathematical Society 124 (1996), 383-387.