National News

Contents

LMS-IMA Working Group
Note from the General Secretary
Mathematical Sciences
EPSRC Mathematics Programme Strategic Advisory Team
Royal Institution Discourse
Whittaker and Watson
Widening Participation in Mathematics, Statistics and Operational Research
Mathematicians Visiting the UK in 2004

 

LMS-IMA WORKING GROUP

Representatives of the LMS and IMA now meet regularly to discuss ways in which the two organisations can co-operate for the good of the mathematical community. A meeting took place on 19 September 2003 and this joint report, the second in the series, is provided for the membership of both societies.

1. It was reported that the design and striking of the David Crighton Medal was proceeding via Fattorini’s; a plaster cast would be available for viewing by Johanna Crighton, and others representing the two organisations. It was proposed that the award be presented to the 2003 recipient, John Ball, at the IMA Presidential Address on 23 June 2004, an open event, followed by a reception.

2. In discussion of the roles played by the IMA and the LMS in support of conferences several points were made, including:

  • Unlike the LMS, the IMA processes conferences to recover all costs and this policy can lead to perceptions that the IMA is less ‘charitable’ than the LMS.
  • Groups of IMA members run conferences from their own organisations and often receive support from the LMS. It was noted that the IMA had recently introduced a modest conference grant scheme aimed at addressing the same need.
  • The LMS feels the need for smaller low-cost meetings and sees no reasons to amend the basis of its support.
  • Outside the academic sector, it was less easy for members to draw on their own organisations to facilitate low-cost meetings. However in many cases the higher registration fee was accepted by the membership as reasonable.
  • Further opportunities for collaboration between the two societies exist, separate from their role in facilitating meetings organised by the mathematics community itself. For example there is a wide range of meetings being arranged across mathematics for different participants. The two societies, in attempting to support meetings in different parts of this multidimensional spectrum, were broadly complementary.

3. Links with overseas and international organisations and mathematicians were discussed.

  • Both organisations have overseas members and their journals are distributed throughout the world. The LMS has reciprocity agreements with some equivalent societies overseas. Other opportunities for international collaboration exist. For instance, neither body at present has formal links with Australia.
  • The LMS Council is considering proposals to establish an International Affairs Committee, to bring together the Society’s international activities. The IMA will be asked to nominate a member to the new committee, as it had for the former IMU Advisory Committee.

4. Future strategy for LMS-IMA relations was discussed, and the following points were made:

  • It was undoubtedly beneficial for the mathematics community that the two organisations were meeting to discuss issues of common interest. No matter what longer-term outcome, it was agreed this level of communication should be maintained.
  • There are clearly strong reasons for looking at closer collaboration, not least in terms of external perceptions of mathematics and our ability to influence policy-formers.
  • The meeting agreed to propose that:
  • the Councils should aim to establish, by discussion among their members, a view within two years on the direction and speed of change in long-term relations between the two bodies;
  • a group (or two linked groups) should be established to draw up a consultation paper, looking at the ways the two organisations could best benefit mathematics by various structural arrangements;
  • no matter what the outcome, the links between the LMS and IMA should be maintained and enhanced.

Norman Biggs
Charles Evans

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NOTE FROM THE GENERAL SECRETARY

On 21 November 2003 the LMS Council discussed the proposal referred to in Item 4 of the report printed above. Council agreed to the proposal in principle, and the details are currently under discussion with the IMA.

Norman Biggs

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MATHEMATICAL SCIENCES

The New Name for EPSRC’s Mathematics Programme

On 1 January 2004, the Mathematics Programme became the Mathematical Sciences Programme. ‘The aim of the change’, said the programme manager, Dr Annette Bramley, ‘is to reflect better the breadth of research and training activities supported by the programme. The portfolio now includes a significant component at the interfaces with other disciplines, and encompasses statistics and operational research as well as mathematics.’

The way the programme operates will not change and it will continue to support programme-specific activities such as the small grant scheme, workshops and post-doctoral fellowships alongside its support for research grants through responsive mode and a small number of managed activities.

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EPSRC MATHEMATICS PROGRAMME STRATEGIC ADVISORY TEAM

The Maths SAT met for the fourth time on 12 November at Polaris House, Swindon. The team received an update on the Balance of Portfolio exercise following the September meetings of Council’s advisory panels TOP (Technical Opportunities Panel) and UP (User Panel). There is a biennial planning cycle that focuses, on alternate years, on programme assurance and on longer-term programme strategy. 2003 is a strategy year during which TOP and UP provide advice to the Chief Executive and Council on financial priorities and provide guidance to Programme Managers on future strategic directions.

In September, TOP and UP considered the fit between the core portfolio and Council’s strategic objectives as set out in the EPSRC Strategic Plan. They also reviewed a number of cross-programme proposals to build on the core portfolio and optimise the allocation of resources within the current baseline.

The feedback on the quality of research being supported by the Mathematics Programme was very positive and the views of the International Reviews of Mathematics and of Operational Research are awaited with interest. The panels endorsed the work that the programme has done to encourage connectivity between mathematicians and users of research in other disciplines and industry/business. However, they felt that there was still a need to continue to improve these interactions and this will remain a priority for the programme. The panels were concerned about the demographics of the academic community, particularly in statistics, where the shortage of researchers is beginning to impact on other disciplines. More generally, TOP and UP were keen that EPSRC should continue to find ways to overcome the conservatism of applicants and peer review, that all programmes should give more attention to public engagement activities and that universities should be encouraged to make full use of the flexibility afforded by doctoral training accounts.

At its October meeting, Council considered the advice from TOP and UP. It also discussed a preliminary proposal from the office for reallocating resources based on the cross-programme bids. Following these discussions, the office will present a full proposal to Council in December, detailing suggested resource allocations to individual programmes for 2004-05 and 2005-06. This will be accompanied by an analysis of the new activities these allocations will enable and the impact of the proposed allocations on existing activities.

Once the resource allocations and the business plans have been finalised and approved by Council they will be published on the EPSRC website.

The SAT had an interesting discussion on the issue of scientific ethics and public trust. EPSRC needs to take appropriate steps to ensure that research proposals are assessed fairly and without bias and that funding is distributed in accordance with clearly articulated principles. The scientific community also should address ethical concerns about its research to retain the support of society and the freedom to explore and develop new areas of science. We would be happy to receive suggestions of any areas of research within EPSRC’s remit where ethical concerns may arise. The SAT also suggested that EPSRC should have the equivalent of a Corporate Social Responsibility statement setting out our policy on these types of issues.

The next item on the agenda was EPSRC’s funding of Statistics. The resources that have been included within the doctoral training accounts to enhance the stipends of PhD students in statistics and operational research were welcomed. In 2004, additional resources will be provided to the Mathematics Programme to continue to provide enhanced stipends in these shortage areas. Some suggestions for novel forms of doctoral training in statistics were made. The SAT suggested that the International Review should provide some indication of the quality of statistics research in the UK compared with international standards. It felt that both EPSRC and the Royal Statistical Society have a role to play in engaging with the research community and encouraging internationally leading statisticians to participate in EPSRC’s responsive mode and its peer review process.

The head of EPSRC’s international section, Jane Sykes, joined the SAT meeting for a discussion of EPSRC’s International Strategy and the UK requirements for Framework Programme 7. Some data on the uptake of EPSRC schemes to support international collaborations was provided – not surprisingly, the Mathematics community is one of the largest users of the overseas travel grant and visiting fellowship schemes.

The final item on the agenda was dissemination of research grant outcomes and knowledge transfer. The SAT provided some feedback on the schemes that were most useful for these types of activities and suggested ways that knowledge transfer could be made more effe

ctive.Finally, the SAT endorsed the change of name of the programme to the Mathematical Sciences Programme from 1 January 2004.

As always, the Mathematics Programme would be happy to receive feedback from the wider mathematics community on any of the issues that were discussed.

Dr Annette Bramley
EPSRC Programme Manager, Mathematics

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ROYAL INSTITUTION DISCOURSE

David Acheson, one of this year’s LMS Popular Lecturers, was the speaker at a Royal Institution Discourse on 31 October 2003. As ever, David gave an excellent talk, entitled 1089, entertaining a large and diverse audience, in the manner customary to these long-established evenings.

Scattered around the RI Library for the event were exhibitions to amuse and inform. The Society’s materials attracted good interest, in particular the videos of the Popular Lectures, including, of course, those of David and Marcus du Sautoy earlier this year.

Another exhibition – models of mathematically-related sculptures by John Robinson – renewed the long association of the Royal Institution with Bangor mathematics and the sculptor.

Ronnie Brown first saw some of John’s amazing sculptures in John’s Freeland Gallery in Albemarle Street, after a Mathematics Masterclasses Organisers’ Meeting in 1985, the Gallery’s second and last year of operation. This led to some of John’s maquettes being presented at the Royal Institution in 1988 and 1992, for Discourses of Sir Michael Atiyah and of Ronnie Brown, and to full size sculptures being shown at the Pop Mathematics Roadshow in Leeds in 1989 and Liverpool in 1990. A website at Bangor (www.cpm.informatics.bangor.ac.uk/), showing over 55 sculptures, was constructed in 1996, supported by Edition Limitée, and was upgraded in 2002 with EPSRC support. This has made John’s work available to the world. Ronnie Brown has lectured on John’s work in Oxford, Toronto (Fields Institute, 90th birthday of Donald Coxeter), Maubeuge, San Sebastian, Paris, Obidos, Bologna, Anglesey and Bilbao.

One of the aims of this association of mathematics and art is to link mathematics, in the public mind and for students, with imagination, rhythm of form, and creativity. Another is to suggest questions on the nature and role of mathematics, and indeed of art.

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WHITTAKER AND WATSON

The text Modern Analysis by E.T. Whittaker and G.N. Watson, published by Cambridge University Press, has been continuously in print for more than a century. This seems all the more remarkable in an age when many textbooks come and go with great rapidity. Whittaker and Watson, as it is most usually called, was first published in 1902, with Whittaker as the sole author. Subsequent editions bear the names of both Whittaker and Watson. The second and third editions followed in 1915 and 1920, and a large number of reprints of the fourth edition have been made since it first appeared in 1927.

E.T. Whittaker (1873-1956) was educated at Manchester Grammar School and Trinity College, Cambridge. Following a Fellowship at Trinity College, he was Astronomer Royal for Ireland from 1906.In 1912 he was appointed to the chair of mathematics at the University of Edinburgh, where he remained for the rest of his career. He was President of the LMS in 1928-29, was awarded the De Morgan Medal in1935, and was knighted in 1945.

G.N. Watson (1886-1965) was also educated at Cambridge, and followed in Whittaker’s footsteps, becoming a Fellow of Trinity College in 1910. He held a chair at Birmingham from 1918 to 1951, and was President of the LMS for the period 1933-35.

The Preface to the fourth edition consists of the following two sentences: ‘Advantage has been taken of the preparation of the fourth edition of this work to add a few additional references and to make a number of corrections of minor errors. Our thanks are due to a number of our readers for pointing out errors and misprints, and in particular we are grateful to Mr E.T. Copson, Lecturer in Mathematics in the University of Edinburgh, for the trouble which he has taken in supplying us with a somewhat lengthy list.’ E.T. Copson (1901-1980), who subsequently married Whittaker’s elder daughter Beatrice, was himself the author of several texts, the best known being Functions of a Complex Variable (1935), which remained in print for about fifty years.

I am grateful to Mr Graham Robertson of Cambridge University Press for the following information about Whittaker and Watson:

  1. Sales for the fourth edition since 1975 exceed 20,000 copies.
  2. The second edition cost 18 shillings, and the fourth edition cost 40 shillings in 1930.

My own copy of the fourth edition, printed in 1958 and purchased in 1959, cost 80 shillings, and the dust jacket bears the following quotation from a review in Nature: ‘Whittaker and Watson has entered and held the field as the standard book of reference in English on the applications of analysis to the transcendental functions.’ This statement would not look out of place if it were repeated today.

George M. Phillips
University of St Andrews

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WIDENING PARTICIPATION IN MATHEMATICS, STATISTICS AND OPERATIONAL RESEARCH

Widening participation has been a concern for mathematics related subjects for some time as this discipline area continues to experience recruitment problems and there are not enough graduates with mathematics related degrees to meet industry's demands.

The Mathematics, Statistics and Operational Research (MSOR) community has already done a lot of work in this area. Links have been developed with schools and the general community, and there have been a number of alternative entry routes provided such as HNDs, foundation degrees and bridging courses to prepare students for degree work.

Students are being supported by a range of appropriate and flexible curricula. A number of new learning and teaching methodologies are being employed. In addition, modes of study have been adapted to cater for the differing needs of students. There is also considerable evidence that the students that have been recruited from this wider pool are realising their potential.

These are the conclusions presented in the booklet Widening Participation in Mathematics, Statistics and Operational Research, by Bill Cox (Aston University) and Penny Bidgood (Kingston University), which has just been published by the LTSN Maths, Stats & OR Network. The booklet examines how lecturers have responded to widening participation, identifies good practice and sets out to disseminate it to the wider community. It contains over 30 different case studies from a wide range of higher education institutions. It groups these under three main headings: recruitment, retention and realising potential.

The examples of practice cover a wide range of outreach activities such as improving links with schools and colleges, publications for school children and providing support and materials for school teachers. A number of alternative entry routes like HNDs and foundation degrees are profiled. There are also a few examples of recruitment aimed at specific groups of people.

The section on retention looks at matching the curriculum to the student intake, student support mechanisms and facilities as well as retention in the USA, retention in FE and improving student achievement in English Higher Education.

This booklet is the latest in the occasional series produced by the LTSN Maths, Stats & OR Network under the heading Learning and Teaching in Mathematics, Statistics and Operational Research (ISSN 1476-1378). The other titles in the series are: Post-sixteen Mathematics within Curriculum 2000, Guidelines for Introducing Group Work in Undergraduate Mathematics, Good Practice in the Provision of Mathematics Support Centres (2nd ed), Flexible Learning in Statistics.

If you would like a copy of any of these booklets, please contact the LTSN Maths, Stats & OR Network (tel: 0121 414 7095, email: info@mathstore.ac.uk). Electronic versions are also available via http://ltsn.mathstore.ac.uk/publications/index.shtml.

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MATHEMATICIANS VISITING THE UK IN 2004

Aberdeen University

Benn, I. (University of New South Wales) Relativity, Jul - Dec ‘04

Bath University

Gutierrez-Penna, E. (National University of Mexico) Bayesian Statistics, Aug ’03 - Aug ’04

Bristol University

Brundan, J. (University of Oregon, USA) Pure Mathematics, 29 Sep - 30 Jan ’04
Rudnick, Z. (Tel Aviv University) Applied Mathematics, 1 Oct ’03 - 30 Sep ’04

Chester College

Bocharov, G. (Russian Academy of Sciences, Moscow) Mathematical Immunology, Apr - Jul ’04

Durham University

Guifloye, B. (IT Tralee, Ireland) Differential Geometry, 26 Apr - 25 May ’04

Exeter University

Emirsajlow, Z. (Technical University of Szczecin) Control Theory, 5 Oct ’03 - 31 Jan ’04
Liao, X. (Chinese Academy of Sciences, Shanghai, China) Astrophysical Fluid Dynamics, 1 Oct ’03 - 1 Mar ’04
Maistrenko, Y. (Ukraine Academy of Sciences) Nonlinear Dynamics, Synchronization, until Jan ’04

Heriot-Watt University

Afrouzi, G. (Mazandaran University, Iran) Differential Equations, Functional Analysis, Oct ’03 - Mar ’04

Hull University

Falkovich, G. (Weizmann Institute for Science, Israel) Mathematical Theory of Turbulence, Mar - Apr ’04
McLeod, J. (Mount Holyoke College) Topological Algebra and Combinatorics, Sep ’03 - Jul ’04

Imperial College London

Barnea, Y. (University of Wisconsin, USA) Algebra, 1 Aug ’03 - 1 Mar ’04
Masumune, J. (Japan Society of the Promotion of Science) Geometry & Analysis of the Dirac & Kohn Laplace Operators, 1 Feb ’03 - 1 Feb ’05
Painov, D. (Ecole Polytechnique, France) Geometry, 1 Apr - 30 Jun ’04
Sibini, P. (University of Southern Denmark) Mathematical Physics: Time Dependent Statistics in Complex Systems, Sep ’03 - Aug ’04
Sohn, S.Y. (Yonsel University Seoul, Korea) Statistics, Dec ’03 - Dec ’04
Zweimuller, R. (University of Salzburg, Austria) Dynamical Systems, 10 Sep ’03 - 31 Jan ’04

Kings College London

Dudulhava, R. (Academy of Sciences of Georgia) Integral Equations, Operator Theory, Partial Differential Equations, Mechanics of Solids, Nov ’03 - Feb ’04

Leeds University (Pure Mathematics)

Callier, F. (Namur University, Belgium) Analysis & Control Theory, 26 Apr - 25 Jun ’04

Leicester University

Diracca, L. (University of Padova) Algebra, Sep ’03 - Sep ’04
Milstein, G.N. (Ural State University) Stochastic Numerics, Mar - Oct ’04
Sun, X. (University of Southwest Missouri, USA) Approximation Theory, Jun-Aug ’04

Liverpool University (Pure Mathematics)

Bryden, J. (University of Southern Illionis, USA) Topology & Representation Theory, Jan - Jun ’04

London School of Economics

Beck, A. (University of Wisconsin) Search Games, Jan - Mar ’04
Gal, S. (Haifa) Search Games, Apr - Jun ’04

Loughborough University

Sutyrin, G.G. (Rhode Island University, USA) Geophysical Fluid Dynamics, Oceanic and Atmospheric Vortices and Fronts, 20 Aug ’03 - 20 Apr ’04

Manchester University

Rafikul, A. (Guwchati, India) Numerical Linear Algebra, 25 Mar ’03 - Mar ’04
Taras, P. (Moscow State University) Algebraic Theory & Combinatorics, 1 Aug ’03 - 31 Jan ’04

Napier University

Kuzmin, G.A. (Institute of Thermophysics, Novosibirsk, Russia) Fluid Dynamics, Turbulence, 15 - 31 Mar ’04

Newcastle University

Agler, J. (University of California, San Diego) Operator Theory, 1 Jul - 31 Aug ’04
Marcantognin, S. (Caracas University, Venezuela) Operator Theory, 1 Jul - 31 Dec ’04

Nottingham University

Ihara, Y. (Kyoto University) Number Theory, Mar ’04
Kato, K. (Kyoto University) Arithmetic Geometry, Spring - Summer ’04
Sato, K. (Nagoya University) Arithmetic Geometry, K-theory, Oct ’03 - Sep ’04
Saito, S. (Nagoya University) Arithmetic Geometry, Spring-Summer ’04
Stix, J. (University of Bonn) Arithmetic Geometry, Oct ’03 - Jan ’04

Oxford University (Mathematical Institute)

Carrillo, C. (Mexico) Mathematical Biology, 1 Oct ’03 - 1 Jul ’04
Johnston, A. (University College London) Mathematical Biology, 1 Oct ’03 - 30 Sep ’04
Kroner, H. (Kaiserslautern) Mathematical Finance, 6 Oct ’03 - 13 Mar ’04
Liu, R.T. (Taiwan) Mathematical Biology, 4 Aug ’03 - 31 Jul ’04
Mackey, M. (Montreal) Physiology, 10 Feb - 18 Mar ’04
Martinez, D. (Spain) Geometry, 1 Oct ’03 - 30 Sep ’04
Mena, F. (Portugal) General Relativity, 1 Oct ’03 - 30 Sep ’05
Meyer-Hermann, M. (Dresden) Mathematical Biology, 1 Oct ’03 - 30 Sep ’04
Nakagaki, T. (Hokkaido University, Japan) Mathematical Biology, Feb - Nov ’04
Scheerlinck, N. (Belgium) Mathematical Biology, 1 Sep ’04 - 28 Feb ’05
Zheng, Z. (China) Scientific Comp/PDE, 1 Mar ’03 - 28 Feb ’05

Portsmouth University

Yaghoobi, M.A. (University of Kerman, Iran) Operational Research, 1 Nov ’03 - 1 Aug ’04

Queen Mary, University of London

Bae, J.S. (Chonnam National University, Korea) Statistics, 10 Feb ’03 - 31 Jan ’04
Filho, J. (Universidade Federal de Lavras, Brazil) Design of Experiments, 12 Jan - 9 Apr ’04
Zochi, S. (Universidade de São Paulo, Brazil) Design of Experiments, 1 Mar ’04 - 28 Feb ’05

Royal Holloway

Schaathun, H.G. (Bergen, Norway) Fingerprinting, 3 Oct ’03 - March ’04
Shin, S. (Sookmyung Women’s University, S. Korea) Cryptography, 2003-04

Salford University

Krillova, I. (Saratov State University, Russia) Bio Mechanics, Sep ’03 - Sep ’04
Nolde, E.V. (Russian Academy of Sciences, Moscow) Asymptotic Methods, Wave Propagation in Solids and Structures, Oct ’03 - Oct ’04

Southampton University

Afshar-Nejad, Z. (Ferdowsi University, Mashhad, Iran) Dynamical Systems 1 Dec ’03 - 30 Sep ’04
Borchers, B. (New Mexico Tech; IPAM, Los Angeles, USA) Semidefinite Programming 8 - 11 Jan ’04
de Oliveira, E. (Bahia Universidad) Clustering Techniques; Three-Phase Simulation Methods 12 Sep ’03 - 31 Aug ’04
Lecuire, C. (UMPA, France) Kleinian Groups and Hyperbolic Manifolds 1 Oct ’03 - 31 Jan ’04
Liyanage, M. (Sri Jayewardedepura University, Sri Lanka) Industrial Applied Mathemtics 1 Feb - 31 July ’04
Morones, R.M. (ITAM, Mexico) Industrial Applied Mathematics 1 Aug ’03 - 31 Jul ’04
Penny, M.P. (QUT, Brisbane, Australia) Modelling of Dye-Sensitive Solar Cells 15 Jan - 6 Feb ’04

St Andrews University

Albert, M. (University of Otago, New Zealand) Combinatorics on Permutations, Sep ’03 - Jan ’04
Hornig, G. (Ruhr-Universität Bochum) Magnetohydrodynamics, Feb - May ’04
Zhugzhda, Y. (University of Moscow) Magnetohydrodynamics, Spring ’04

Strathclyde University

Belyakov, V.A. (Landau Institute of Theoretical Physics, Moscow) Nonlinear Optics in Chiral Liquid Crystals, Electromagnetic Waves in Periodic Media, Solid State Nuclear Physics, 1 Jun - 31 Aug ’04

UMIST

Mendez, V. (Universitat International de Catalunya, Spain) Dynamical Properties of Reaction-Diffusion Fronts, 1 Apr - 30 Jun ’04
Reisen, B.V. (Universidade Federal do Espirito, Brazil) Long Memory Models, 10 Nov ’03 - 30 Apr ’04
Yalcinkaya, S. (METU, Ankara, Turkey) Pure Mathematics, 25 Jul ’03 - 31 Jul ’04

University of Wales, Aberystwyth

Ervin, V.J. (Clemson University, SC, USA) Viscoelastic Flow, Numerical Analysis, Jul - Aug ’04
Mullen, G.L. (Pennsylvania State University, USA) Design Theory, Finite Fields, Hypercubes, Jun - Jul ’04
Owens, R.G. (École Polytechnic Féderéle de Lausanne, Switzerland) Viscoelastic Flow, Spectral Methods, May ’04

University of Wales, Swansea

Levendovskii, S. (University of Texas) Pseudo-differential Operators & Markov Processes, Applications to Finance, Mar - Apr ’04

Warwick University (Mathematics Institute)

Brassesco, S. (Instituto Venezolano de Investigaciones Cientificas) Stochastic Analysis, 21 Aug ’03 - 31 Aug ’04
Choi, Y. (Kyungpook National University) Hyperbolic Geometry, 16 Oct ’03 - 15 Oct ’04
Ingallis, C. (University of New Brunswick) Noncommutative Algebra, Algebraic Geometry, 1 Sep ’03 - 31 Aug ’04
Lecuire, C. (UMPA, ENS-Lyon) Hyperbolic Geometry, 1 Feb - 3 May ’04
Liu, Y. (Yangzhou University) PDEs & Nonlinear Dynamics, 25 Oct ’03 - 30 Oct ’04
Marden, A. (University of Minnesota) Kleinian Groups, 15 Mar - 15 May ’04
Moori, J. (University of Natal) Algebra, 30 Jul ’03 - 15 Jan ’04
Shen, Y. (Suzhou University) Geometric Analysis, 10 Jul ’03 - 10 Jan ’04

Warwick University (Statistics)

Jayasekara, L. (University of Rumana, Sri Lanka) Contingency Tables, Tests on Contingency Tables, 1 Oct ’03 - 31 Mar ’04

York University

Beresnevitch, V. (Minsk University, Belarus) Number Theory, Oct ’03 - Aug ’04
Skrigonov, M. (Steklov Institute, St. Petersburg, Russia) Number Theory, Nov - Dec ’03

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