To celebrate the occasion ICMS gave a reception at India Street on the evening of 6 April 1994. Earlier that day I had the pleasure of participating in the Edinburgh Science Festival, giving a lecture at the Royal Society of Edinburgh on "Mathematical Logic in the 20th Century". This was essentially an Inaugural Lecture to mark my appointment as the ICMS Scientific Director. The lecture and reception gave me a welcome chance to meet many of ICMS's friends and benefactors from the worlds of academia, business, commerce and government. During the same period I made the acquaintance of two very distinguished participants in the Science Festival: Dr Neil Lane, Director of the US National Science Foundation, and Professor Manuel Patarroyo, from the Instituto de Immunologia in Bogota, the Edinburgh Medallist, famous for his work on a malaria vaccine. Both were enthusiastic about ICMS. Dr Lane, as a physicist and Maxwell enthusiast, enjoyed a visit to India Street. Professor Patarroyo, whose charm will be remembered by all who heard him, is keenly interested in interaction with ICMS.
After the festive opening came the adjustment to new working conditions and the numerous arrangements needed for the running of frequent research workshops. This is mainly the responsibility of Lucy Young, our Executive Director, who, like me, joined ICMS towards the end of 1993. To Lucy, and to Elmer Rees, the unflagging Chairman of the ICMS Executive Committee we owe the smooth transition to India Street.
Eight months on, we see that 14 India Street is well suited to house workshops of about fifty people. Our very first such event, on Harmonic Analysis, set high standards for all that will follow. The centrepiece of this years activity is a series of workshops on Mathematics in Medicine, and a wide range of other events ensures efficient use of our new facilities. We shall also be welcoming the first of our Developing World Scholars, Professor Joshi from India, who will work at India Street. Next year we welcome Professor Jerrold E Marsden, Berkeley as the new Chairman of the Programme Committee.
We were very fortunate to appoint, in April 1994, Louise Williamson, as an assistant to Lucy Young. Very soon after Louise's arrival, Lucy became seriously ill and was on sick leave for months. (Happily she is now almost completely recovered). Louise rose to the occasion, and the success of the Harmonic Analysis workshops is largely due to her exceptional efforts in collaboration with the scientific organizers, Tony Carbery and Alastair Gillespie. Later in the year, Michael Moss joined us to assist with fundraising and the India Street office is now a very busy (and cheerful) place.
In this editorial I have been highlighting practical matters rather than grander issues of the philosophy of ICMS. The latter have been set out before, and will be again, for example as we move towards the major responsibilities associated with ICIAM 99. Next year we will be involved prominently in the celebration of the 50th birthday of UNESCO, and our friends and supporters will hear about this in detail before long. This is one of several areas of cooperation with the James Clerk Maxwell Foundation. We will continue to co-ordinate our scientific activity with other international research centres, while preserving our own style.
Last year Stirling University became an Associate Member of ICMS and its representatives are already contributing to our plans. For me this year, one of the main pleasures was meeting three remarkable Principals, Professors MacFarlane, Forty and Sutherland, all of whom have shown strong commitment to ICMS. Professor Forty has just begun what promises to be a very active retirement and we are grateful for his continued involvement with us. On a more personal note, I can say that it was because of ICMS that Stewart Sutherland and I met again thirty years after our student days together at Cambridge. We are very glad that he has been able to join our Steering Committee and all at ICMS congratulate him heartily on his recent Knighthood.
Having been part of ICMS for a year, I am keenly aware of the generosity of the many people in academic and public life who give freely of their time and energies to ICMS, because they believe, as I do, that it is a good thing for science, education and society in our part of the world. I am thinking mainly of Elmer Rees, John Ball, Robin Knops, Chris Eilbeck, Geoffrey Boulton and Ian Wall, in Edinburgh, and of other academics who regularly come from elsewhere for our planning meetings. We congratulate John Mavor, a long serving member of the Executive Committee, on becoming Principal of Napier University and hope that we will retain close links.
We have this basis of goodwill, we have our own premises and there is no shortage of scientific challenges. We are hoping now for steady consolidation of our financial base, with the help and advice of the commercial and industrial communities.
Professor Angus Macintyre FRS, Scientific Director
Participants in ICMS activities have already indicated that the association with James Clerk Maxwell is an inspiring influence. The James Clerk Maxwell Foundation, with which ICMS cooperates, has plans to use the meeting room as a museum to commemorate Clerk Maxwell. The room is currently lined with family portraits. James Clerk Maxwell's achievements are outlined briefly on page 25 of this newsletter.
The move to India Street would not have been possible without the continuing support given to ICMS by the following organisations:
The workshop attracted an international audience including over 50 researchers from all aspects of the field as well as participants with backgrounds in biology, physics, engineering and finance.
The programme took the form of two weeks of intensive study with some visitors in residence for longer. The two weeks were broken into sessions focusing on Measure Valued Processes, approaches to Stochastic Partial Differential Equations via stochastic calculus, and Mean Field Theory. The meeting succeeded in its aim to bring together workers in these three major areas and led to many fruitful interactions. Two days were devoted to applications, with contributions from biology, physics and engineering. There was also an opportunity to learn about the efficient numerical simulation techniques now available.
The programme incorporated long discussion sessions between lunch and the afternoon talks. These were very successful in establishing new collaborations some of which will be reported in a proceedings volume. These sessions were also extremely valuable for the graduate students and young postdoctoral researchers attending the meeting, not only in facilitating contact with leading researchers in the field, but also in allowing them to develop a network of their own.
Thanks are due to EPSRC for providing financial support and of course to all the participants of this productive and thoroughly enjoyable meeting.
Overall, more than 200 mathematicians from 25 countries participated in the programme, the main focus of which was the interaction between harmonic analysis and partial differential equations. A large number of leading experts in both areas visited Edinburgh during the four months, some staying for substantial lengths of time and others for shorter periods.
The programme started with an Instructional Conference, held at the University of Edinburgh and attended by almost a hundred mathematicians, forty of whom were graduate students. Introductory courses were given by A. Carbery (Sussex) and F. Soria (Madrid), followed by more advanced ones by C.E. Kenig (Chicago) and E. M. Stein (Princeton). There was universal praise from the participants for the high standard of all four courses. After the Instructional Conference, the activities moved to 14 India Street, where ICMS had just taken up occupancy. Here, an on- going research programme proceeded in a congenial and friendly atmosphere, with between ten and twenty participants resident at any one time. An informal seminar was held most afternoons.
Numbers swelled to around 60 during each of two workshops which punctuated the programme. The first, from 5 to 11 June, focused on oscillatory integrals, curvature and applications in hyperbolic and dispersive pde's, whilst the second, from 17 to 23 July, concentrated on elliptic pde's and related areas of harmonic analysis. The formal talks at the workshops were limited to allow enough time for informal discussions amongst those participating. Judging by the general buzz of activity, every advantage was taken of these arrangements.
The organizers, A. Carbery and D. E. Edmunds (Sussex) and T. A. Gillespie (Edinburgh), benefited greatly when planning the programme from the advice of E. B. Fabes (Minnesota), C. E. Kenig and E.M. Stein. The bulk of the funding came from EPSRC, with additional support from the Edinburgh Mathematical Society, the Royal Society of Edinburgh and the European Union HCM programme in Fourier Analysis. Thanks are due both to the funding bodies and to all who participated in what was an extremely successful and productive four month programme.
This summer school and workshop, forming part of the Nonlinear Systems programme of the European Science Foundation, Strasbourg, was adopted by the Human Capital and Mobility Programme as a Euroconference. It was held at the James Clerk Maxwell Building , University of Edinburgh and organised by David Parker, John Byatt-Smith and Noel Smyth (University of Edinburgh) . Seven series of principal lectures were delivered by A. B. Aceves (Albuquerque), J.N. Elgin (Imperial College, London), R. Indik (Tucson), W.L. Kath (Northwestern), J. Lega (Nice), L.F. Mollenauer (A.T&T. Bell Labs), A. C. Newell (Tucson). Invited lectures were given by J.S. Aitchison (Glasgow), D. Anderson (Chalmers), J.M. Arnold (Glasgow), A.D. Boardman (Salford), M. Brambilla (Milan), N.J. Doran (Aston), W.J. Firth (Strathclyde), J.P. Gordon (A.T. & T), R.G. Harrison (Heriot-Watt), H.A. Haus (M.I.T.), C.K.R.T. Jones (Brown), D.J. Kaup (Clarkson), Yu.S. Kivshar (Canberra), S. Koch (Marburg), B.A. Malomed (Tel Aviv), J.V. Moloney (Tucson), G-L Oppo (Strathclyde), S. Trillo (Rome), S. Wabnitz (Rome) and R. W. Ziolkowski (Tucson). There were 30 research students and 14 post-doctoral researchers among the 105 participants from 20 countries; the majority gave lectures or presented posters.
The principal themes of the programme were the modelling and exploitation of nonlinearity in optical telecommunication, switching and laser systems. Major lecture topics included perturbed scalar and vector solitons in fibre-optic transmission systems, the practical implementation of optical soliton ultra-long distance communications, nonlinear mode structure in fibre and planar waveguides, nonlinear steering and switching of light beams, optical patterns and chaos in laser cavities, dynamical systems techniques, the theory and possible exploitation of dark solitons and numerical issues of large-scale computation. During the workshop, investigation groups on most of these themes were formed leading to new collaborations and consolidating existing partnerships. Reports from these groups were issued to all participants (and are available from ICMS) and both survey the existing literature and outline research directions resulting from the workshop.
Participants were very appreciative of the excellent opportunities to discuss problems raised during the lectures. Thanks are due to the range of sponsors that included The European Science Foundation, European Union (H.C.M. programme), O.N.R. (U.S. Navy), E.O.A.R.D. (U.S.A.F.), E.R.O. (U.S. Army), BNR (Europe) Ltd, The Royal Society of London and International Science Foundation (Soros), City of Edinburgh District Council, University of Edinburgh and Edinburgh Mathematical Society.
This year-long programme aims to bring together mathematicians and medical experts to study problems relevant to certain areas of medical science. The programme is divided into two sections each containing four workshops. The three workshops in 1994 have been very successful and reports on these are given below. There has been widespread interest in each of the remaining workshops with enquiries coming from both mathematicians and medical scientists.
Support for this programme has been received from a number of sources including the following organisations:
The ICMS programme "Mathematics in Medicine" got off to a very good start with a 3-day workshop on "Modelling the Heart" attended by 20 researchers, mathematicians and physiologists from all over the world. A total of 7 plenary talks were given during the workshop, supplemented by various contributed talks.
The workshop began on Tuesday 25th October, with the morning session being devoted to Mechano-electric feedback. Professor Max Lab opened with a very interesting presentation of recent work which has begun to shed light on the potential influence of mechano-electric feedback in heart physiology. This was followed by a second talk devoted to the mathematical modelling of mechano-electric feedback by Dr. Glenna Bett. During the afternoon, Professor Sir Denis Noble gave an exciting presentation concerning the modelling of the heart at a cellular level with demonstrations being shown using the OXSOFT package.
Wednesday 26th October was devoted to reentry in cardiac tissue and Professor Leon Glass started the day with his talk on nonlinear dynamics of reentrant arrhythmias followed by Dr. Arun Holden who demonstrated how, in theory, it is possible to control reentrant activity in models of cardiac tissue. Both talks generated much discussion, and the scheduled contributed talks for the morning session were postponed until the afternoon.
Thursday 27th October focused attention on wave propagation in cardiac tissue and Professor Brian Sleeman gave the first talk which was concerned with the mathematical modelling of wave propagation in excitable media with particular attention being given to the heart. This was followed by a stunning presentation by Dr. A. Panfilov who showed some video footage of spiral and scroll waves in a 3-dimensional anatomical model of the heart. The final presentation of the meeting was given by Dr. J. Hyde who presented a mathematical model of cardiac cell excitation using the connection machine simulations based on the model of Noble. The afternoon session was taken up with various discussions on funding opportunities for mathematical cardiology in the UK and Europe, controlling chaos and granularity versus continuity in propagation - is cardiac tissue coupled cells or a medium?
This very successful workshop occupied four and a half days, 9.00am to 6.00pm Monday to Thursday and 9.00am to 12.45 pm Friday. The aim was to give a relatively small number of workers in the field the opportunity to present and discuss their current work thoroughly, with each other and additional participants, without holding back on the mathematical and computational detail. The workshop was organised under 5 headings, each of which occupied approximately one day.
The first day was concerned with Modelling the Coronary Circulation. Jos Spaan from Amsterdam set the scene with two immensely informative lectures, in which he discussed both mechanical and control aspects of coronary perfusion, showing how vital is the close coupling between modelling and experiment. After lunch Colin Caro (IC London) demonstrated the link between wall shear stress and atherosclerosis, and emphasised the complexity of the real 3D geometry of arteries which must be modelled carefully. Other invited talks were on fluid mechanics, modelling coronary arteries as (a) collapsible tubes and (b) curved tubes of non- uniform and time-dependent curvature, and investigating pulse wave propagation. There was a contributed talk on cardiovascular control and a film on microembolism in the retina.
The Tuesday was Collapsible Tube day. Tim Pedley (Leeds) set the scene with a brief outline of the physiological and experimental background, and Jim Grotberg (Northwestern) surveyed the progress that has been made in modelling forced expiration and flutter in airways. Most of the rest of the day considered flow and self-excited oscillations in laboratory experiments, a succession of talks (notably by Oliver Jensen (Newcastle) and by several members of the Leeds group) demonstrating how understanding has advanced in recent years, via 1D, 2D and 3D models. An interesting instability analysis was presented by Jitesh Gajjar (Manchester).
Most of the third day was concerned with Computational Methods, though it began with two contributions from London on modelling flow in the vasa recta of the kidneys and in the glycocalix, the absorbed layer of large molecules that lines the endothelium of blood vessels. The computational speakers, notably Owen Tutty (Southampton), Denis Doorly (IC), and Mike Collins (City), successfully got the message across that the results of computations on new and difficult problems (such as time-dependent flow in complex geometry with unknown elastic boundaries) should not be believed unless every conceivable check and test has been made, including solving the problem using two independent methods.
The Thursday was devoted entirely to Pulmonary Modelling. We heard a masterly survey of the whole field from Jim Grotberg and another excellent talk on surface tension and surfactant effects by Oliver Jensen. There were also fascinating contributions on mixing in the airways, from Peter Hydon (Northumbria) and Christopher Phillips (IC), and on modelling lung structure, also from the IC group (Bob Schroter and Christopher Phillips).
On the Friday morning there were three somewhat disparate talks on Transport Processes. Peter Winlove (IC) gave a brilliant survey of mechanics and transport in connective tissue; Evelyn Carew (Leeds) talked about a new model of peristaltic pumping which includes a description of active muscle contraction; and Dimitris Parthimos (Cardiff) showed us fascinating data and models of chaotic behaviour in arterial vasomotion.
Participants enjoyed the convivial if hard-working atmosphere of the work-shop. The organisers were especially grateful to their overseas colleagues, Professors Jos Spaan and Jim Grotberg, for their splendid contributions; Jim Grotberg, who stayed all week, was a particular source of stimulation and insight to all the young (and not-so-young) scientists present.
The ICMS workshop on Biomechanics was attended by participants from various fields of research including mathematics, biology, bio-engineering, mechanics and medicine.
The workshop began with the opening talk by Professor NcNeil Alexander, FRS, of Leeds University who gave a very interesting and animated exposition of the mechanics of human locomotion. This was followed by a presentation by Prof. T. McMahon (Harvard) whose talk was entitled "Animal Impacts". The first half dealt with the modelling of how people fall and fracture their hips (and how to try and prevent this by developing a protective patch to wear). During the second half he focused on the mechanics of the so-called Jesus Christ lizard which has the ability to walk on water. Both talks generated much discussion. The afternoon session consisted of a presentation by M. Chaplain (Bath) concerning the mechanics of the growth of solid tumours with particular attention being paid to the processes of invasion and metastasis. This was followed by a very fruitful discussion session on tumour growth led by Prof. R. Skalak (UCSD) who developed some of the points raised by Dr. Chaplain.
Invited speakers:
E H Sage (Seattle, Washington), J Davidson (Vanderbilt), W Lindblad (Wayne State), P Maini (Oxford), J Sherratt (Warwick), R Clark (StonyBrook),
Wound healing, ie the repair of damaged tissue, has been known and studied since the times of the pharoahs of Egypt and is still of great importance today both from a clinical point of view and more recently in plastic surgery. Recent biological advances into the underlying mechanisms responsible for wound healing have led to an increase in the development of mathematical models. One goal of the modelling would be to predict exactly how a particular wound is going to heal or what the shape of the subsequent scar will be. It is hoped that the mathematical modelling of wound healing may suggest the optimal technique to use in order to minimise scarring. Problems arising from several areas eg epidermal wounds, dermal wounds, scarring, role of growth factors, angiogenesis will be discussed.
Topics:
Invited Speakers:
J Folkman (Children's Hospital, Boston), R Jain (Harvard), R Sutherland (SRI International), J Adam (Old Dominion), H Acker (Dortmund), W Mueller-Klieser (Mainz), R Lefever (Brussels) V Kuznetsov (Moscow)
Improvements in the treatment of various forms of cancer are dependent on the accuracy of diagnosis of the presence, type and extent of a tumour. The information provided by routine histological techniques is not always precise. A quantitative measure of the factors which are known to influence the prognosis of a particular type of malignant tumour is often required. It is difficult to establish firm criteria which apply to cancers in general; elaborate criteria have been set up for most of the comon forms of cancers. Mathematical modelling applied to these areas of medicine can offer insights into the problems being studied and stimulate further research hitherto overlooked or unidentified by those in the medical profession.
Studies and experiments carried out in vitro on multicell spheroids, whose structure is very similar to certain solid tumours found in vivo eg carcinoma, have yielded much insight into the structure, cell kinetics and early development of avascular tumours. Mathematical models of the immune system's response to tumours and models for vascular growth will be discussed as well as recent work carried out to investigate the relationship between the so called "fractal dimension" of a tumour boundary and the invasive potential of that cancer. The interplay between experimental studies and the corresponding mathematical models which have evolved in this area will be discussed.
Topics:
Invited speakers:
G Webb (Vanderbilt), Z Agur (Oxford), O Arino (Pau), S Michelson (Syntex Discovery Research), L Pilz (Heidelberg).
Chemotherapy, and more generally drug-uptake in the body as a whole, is an area where the application of control theory can be of great help to the medical researchers. It is of vital importance that drugs are administered in a manner which optimises their uptake in the body but one also wishes to minimise damage to healthy cells. Modelling regimes of drug intake (eg administering the drug at different times with different doses) using mathematical techniques can determine the advantages and disadvantages of different regimes and can also suggest the optimal regime. This has particular applications to chemotherapy scheduling.
Topics:
Invited Speakers:
N Wright (ICRF/Hammersmith), C Potten (Paterson Institute for Cancer Research) A Columbano (Cagliari), L Mallucci (Guy's Medical School), O Iversen (Oslo)
One of the main diffences between a cancer cell and a normal cell is that it has escaped the normal mechanisms that control its proliferation and division. A deep understanding of the cell-cycle is therefore vital for an understanding of why cells become and remain cancerous. Mathematical models of cell kinetics (age structured population models, cell migration models, models of growth factors and inhibitory factors etc) provide an insight into the growth characteristics of tumours.
Topics:
Invited Speakers:
J Demongeot (Grenoble), W Jaeger (Heidelberg), W Alt (Bonn), C Jennison (Bath), P Green (Bristol).
Monitoring the behaviour of the organs and functions of the body is best carried out with non- invasive imaging techniques. Recent technological advances make it possible to extract objective and quantitatively accurate information from 3-D images currently produced by techniques such as CT, MRI, PET, SPECT and Ultra Sonic imaging. Indeed there now exist software packages which, by utilising the differential geometry of the surface under observation, permit a detailed investigation of the properties of the object as a whole (eg analysis of mammograms and solid tumours in the breast). This poses many challenging mathematical and diagnostic problems. As a particular example, by combining information on the curvature of a solid tumour with results regarding the strain energy function, it is possible to provide a mathematical description of the important clinical processes of staging and grading cancers. These same techniques have also been successfully used in modelling the deformity of the human heart; this illustrates the general principle that the same mathematical technique can often be used in a number of seeminigly unrelated areas. Thus the topics dealt with in this workshop also relate to the first half of the year which was devoted to mathematics applied to physiology.
Topics:
The past decade has witnessed much progress in the formulation and testing of mathematical models of the spread and control of infectious diseases. The theoretical framework is based on the description of the processes that control the typical course of infection within the human host and those that determine spread in communities of people. Models increasingly reflect the many heterogeneities that influence the dynamics of pathogen growth and spread. These include spatial, behavioural and genetic factors. The talk will focus on the theory developed to describe the transmission dynamics of viral and bacterial childhood infections, such as measles, rubella, mumps and pertussis. A particular emphasis will be placed on the role of this body of theory in the design of mass vaccination programmes and public health policy. Examples will also include studies of the transmission dynamics and spread of the AIDS virus.
Professor Roy Anderson, of the Wellcome Centre for Infectious Disease Epidemiology who is Linacre Professor of Zoology at Oxford University, will be giving a public lecture in the Royal Society of Edinburgh at 4 pm on 6th April 1995. This will form part of ICMS's contribution to the Edinburgh International Science Festival. For further information and tickets contact Louise Williamson at ICMS.
Organisers: S Krantz (St Louis), N Sibony (Orsay), T Bailey (Edinburgh), E Rees (Edinburgh)
An instructional course on analytic and geometric aspects of the theory of Several Complex Variables.
There will be a number of short series of lectures given by leading experts in the field. The course will start with a series of introductory lectures on very basic material accessible to those with little knowledge beyond one complex variable; this will be given by Professor R Narasimhan (Chicago) and will start on the afternoon of Sunday 19 March.
During the period 20 March to 25 March, the following courses will also be given:
Anyone interested in attending can obtain further information or application forms from Louise Williamson, ICMS.
A research workshop on the above topic will be held in Edinburgh and supported by a grant from the Engineering and Physical Sciences Research Council. The workshop will take place on 19 - 20 April 1995, and will be followed by an Open meeting on April 21. The general objectives are as follows:
- to discuss problems of statistical and mathematical interest within the scope of Artificial Neural network (ANN) research;
- to discuss statistical concepts and tools that expand the technology of ANN research;
- to try to identify areas, if any, where ANNs outperform standard statistical methods;
- to enhance collaborative research between the two communities.
Invited speakers will include Leo Breiman (Berkeley), Phil Brown (Liverpool), David Hand (Open University), Trevor Hastie (ATT and Stanford), Nathan Intrator (Tel Aviv), Michael Jordan (MIT), Jim Kay (SASS), David Lowe (Aston), David Mackay (Cambridge), Radford Neal (Toronto) and Brian Ripley (Oxford). In addition, a small selection of case studies will be presented, submitted as entries for a 'competition'. The meetings will form part of the Edinburgh Science Festival.
Participation in the Workshop has been predominantly by invitation, with some priority given to research students. Limitations on numbers have, regrettably, led to a high proportion of the direct applicants being unsuccessful. However, there will be much less restriction on numbers for the Open meeting on April 21, also to be held in Edinburgh. The speakers for this will be drawn largely from those involved in the workshop. In general, the material presented will be at a more expository level than that in the workshop, but a report on the achievements of the workshop will also be presented. For details of the Open meeting, contact ICMS.
Many engineering structures consist of one-dimensional (rods), two-dimensional (plates and shells) and three-dimensional parts that are connected together to form a multibody. Recent mathematical advances, in particular due to PG Ciarlet, H Le Dret, VG Maz'ya and V Koslav, have led to an improved understanding of how to analyse the junctions between the component parts of multibodies, and to predict their overall static and dynamic behaviour.
The aim of the conference is to bring together participants from industrial and academic backgrounds, in order to contrast approaches, exchange ideas and confront open problems. This goal will be achieved through general lectures that will be accessible to a wide audience and through ample room left for informal discussion. Speakers are expected to include: M Bernadou (INRIA-Rocquencourt), PG Ciarlet (Paris VI), VA Koslov (Linkoping), JL Lions (College de France), VG Maz'ya (Linköping), AB Movchan (Bath), R Ohayon (Conservatoire National de Arts de Arts et Metiers), G Panasenko (Saint Etienne), J Periaux (Avions Marcel Dassault).
The conference is organized by PG Ciarlet and H Le Dret (Paris VI). For further information contact J M Ball, Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS Tel 0131-451 3227, Fax 0131- 451 3249, E-mail J.M.Ball@ma.hw.ac.uk
Modern quantitative techniques allow one to be precise about what is risk, who should carry it and how it can be managed most effectively. This increases the responsibility of pension fund trustees and their managers to be much more specific than in the past about what their objectives and rules really are. This meeting will concentrate on the interaction of quantitative financial engineering and modern actuarial approaches.
The meeting will last two days and sessions will be composed of talks and organised discussion. Topics will include:
For further information contact:
Prof T J Lyons, Department of Mathematics, Imperial College, Huxley Building, Queen's Gate, London SW7 2BZ. Tel 0171-594 8489 Fax:0171-594 8517 E-mail:t.lyons@ic.ac.uk Dr A J G Cairns, Dept of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS. Tel:0131-449 3245 Fax:0131-451 3249 E-mail:andrewc@cara.ma.hw.ac.uk Ms L Young, ICMS, 14 India Street, Edinburgh EH3 6EZ. Tel 0131- 220 1777 Fax 0131-220 1053 E-mail: l.young @ed.ac.uk
This workshop forms part of the celebration in Edinburgh of the 50th anniversary of the founding of UNESCO. It will focus both on significant new mathematical developments in fluid mechanics, and on important problems in fluid mechanics and its applications which are in need of such developments.
The workshop will consist of short expository lecture courses by distinguished researchers including P. Constantin (Chicago), P-L. Lions (Paris) and A. J. Majda (New York), together with individual invited lectures by other leading mathematicians and scientists.
Participation in the workshop will be by invitation only; those interested in participating and receiving further information should write to J. M. Ball, Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS Tel 0131-451 3227 e-mail J. M.Ball@ma.hw.ac.uk
The workshop will have three main themes, firstly to bring together the different communities of scientists and statisticians involved in the collection and analysis of environmental impact data and hence to promote discussion on data requirements; secondly to identifiy areas for development of statistical methodology and finally to enhance collaborative work and cross-fertilisation . A number of key speakers from the legislative and regulatory bodies and academic institutions will be invited.
Further details can be obtained from Dr Marian Scott, Department of Statistics, University of Glasgow, Glasgow G12 8QW Tel 0141 339 8855 ext 5125, fax 0141 330 4814, email marian @stats.gla.ac.uk
An ICMS instructional conference. Organisers: A W Knapp (Stonybrook), M. Duflo (Paris), L Clozel (Paris), T N Bailey (Edinburgh).
The first week will be a series of introductory lecture courses. The second week will cover more advanced topics, including automorphic forms and their connection with number theory.
For further information contact: Dr T N Bailey, Department of Mathematics, Edinburgh University, Tel. 0131 650 5068, Fax: 0131 650 6553, email tnbailey@ed.ac.uk.
In recent years there has been an explosion of interest in Computational Number Theory, as a consequence both of the availability of much more powerful computing facilities, and of the upsurge in interest in constructive mathematics. In Spring 1996 we plan to hold a workshop on one part of this field: "Curves and Computation". The conference will cover computational aspects of curves of small genus (largely elliptic curves), more general curves, as well as applications (e.g. to coding and cryptography), and connnection with symbolic algebra. For further details contact:
Dr C J Smyth, Edinburgh University, Tel. 0131-650 5054, Fax 0131-650 6553 e-mail chris@maths.ed.ac.uk or Dr J E Cremona, Exeter University, Tel. 01392 263986, Fax 01392- 263997, email cremona@maths.ex.ac.uk
Adaptive methods are generally used with finite element and finite volume methods and attempt to distribute the mesh points throughout the solution domain of a problem in such a way that they are concentrated in regions with important local fine detail and rapid changes and sparse where the solution changes slowly. The savings in computer storage and effort can be very significant, and thus allow more detailed and complex simulations to be performed in many areas of science and engineering. Unfortunately there are practical and theoretical barriers to overcome in the implementation of these techniques, despite the simplicity of the basic idea. The design of an optimal mesh distribution strategy must take into account the mathematics of stability and convergence, the computer science of handling large, complicated data structures (on serial and parallel computers) and the engineering of the final application.
We plan to run a specialist workshop and a short conference in May 1996 to bring together contributors from the various disciplines involved in this work. For further information contact:
Dr. M. Berzins, Computer Science, Leeds University Tel 0113-2335457, Fax 0113-2335468, e-mail martin@scs.leeds.ac.uk. or Dr. D. B. Duncan, Mathematics, Heriot-Watt University Tel 0131-451 3244, Fax 0131-451 3249, e-mail dugald@ma.hw.ac.uk.
The workshop will be devoted to the interplay between geometry and topology arising in the study of the global geometry and topology of moduli spaces and the topology of special Riemannian geometries.
There has been much progress in the study of a number of questions in quaternionic geometry, in Einstein manifolds, and in the topology of moduli spaces of instantons, monopoles, and holomorphic maps. There are close relationships between these topics. Quaternionic geometry is the higher dimensional generalization of the concept of self-duality in four dimensions. The analysis of the global geometry and topology of certain analytic moduli spaces, which culminated in the solution of the Atiyah-Jones conjecture and of Segal's conjecture for stability of holomorphic mapping spaces, has been an important landmark. It is to be expected that the successful techniques in these two areas should have fruitful interaction; for example, the relation between certain quaternionic mapping spaces and instanton moduli spaces is of interest in this regard. The following topics will be amongst those that will be discussed during the workshop:
10 to 14 June 1996: Topology of special Riemannian geometries. Including a general series of lectures on The foundations of Hyperkähler, Quaternionic Kahler, and 3-Sasakian Geometry.
24 to 28 June 1996: The global geometry and topology of moduli spaces. This will include a general series of lectures on Iterated loop spaces and the topology of continuous mapping spaces.
Organisers are: K. Galicki (New Mexico) and B. Mann (New Mexico and Edinburgh) For further details contact ICMS.
There will be an eight week programme on Nonstandard Analysis and its Applications. Nonstandard methods are currently being effectively used in analysis, differential equations, probability and stochastic analysis, mathematical physics and mathematical finance theory. This programme will place particular emphasis on making the power of nonstandard methods more widely known and available amongst the community of mathematical researchers. The programme will have three components, as follows:
1 - INSTRUCTIONAL CONFERENCE (Probable dates 1 - 13 July)
This will be an intensive Instructional Conference for research mathematicians wishing to learn the basics of nonstandard techniques and the range of applications of these tools. This will be aimed at the postdoctoral level, but will be accessible to good research students. The topics it is proposed to cover are: Foundations of nonstandard analysis and nonstandard models, basics of nonstandard real analysis, topological applications, Loeb measure theory, applications in probability and stochastic analysis, applications in functional analysis, applications to differential equations (ODEs, PDEs, SDEs and SPDEs), applications in mathematical physics and mathematical finance theory.
The provisional list of those who will be lecturing includes: L. Arkeryd, M.Capinski, N.J. Cutland, C.W. Henson, R. Jin, H.J. Keisler, P.E. Kopp, T. Lindstrom, P.A. Loeb, D.A. Ross. Lectures will be supported by tutorial and discussion sessions.
2. RESEARCH WORKSHOP (Probable dates 14 July - 17 August)
A number of mathematicians (nonstandard analysts and others) will be in residence, based in India Street, for a period of dissemination, stimulation, interaction and collaboration. The participants will include experts who are aware of important mathematical issues and problems ("pure" of "applied") that are appropriate for nonstandard attack, who are interested to join forces with nonstandard experts to discuss and begin collaborative work.
3. RESEARCH SYMPOSIUM (Probable dates 18 - 24 August)
This will be an open meeting, with invited speakers and contributed talks reporting on recent research in nonstandard analysis and its applications.
This programme is being organised by N.J. Cutland (Hull), L. Arkeryd (Goteborg), C.W. Henson (Illinois). For further information contact N.J. Cutland, School of Mathematics, University of Hull, Hull HU6 7RX Fax 01482-466218, e-mail: n.j.cutland@maths.hull.ac.uk
Associated Programmes 1995
These are programmes for which ICMS provides minimal support but has not been fully involved in their planning.
Scientific computation Geometry and robotics Risk analysis of disasters Reliability theory and code verification Models for friction and damage. Control theory Modelling and inference in interactive systems Mathematics and large scale computation Computational aspects of operations research
The Scientific Director welcomes opportunities to discuss ideas and proposals for ICMS activities. Proposals should be no longer than two sides of A4 paper and when accepted they form the starting point for the preparation of more detailed plans. Proposals may be received at any time but for full discussion at the 1995 meeting of the Programme Committee they should be received by 17 March 1995. They should be sent to Prof A J Macintyre FRS, Scientific Director, ICMS (Proposal), 14 India Street, Edinburgh EH3 6EZ E-mail: icms@maths.ed.ac.uk
Mathematical Sciences at The University of Stirling
The University of Stirling has affiliated to ICMS in the expectation that Associate Membership will prove of mutual benefit to the two institutions. For its part the University hopes to consolidate and expand the contacts between its staff and all others who contribute to ICMS activities. To facilitate this process there follows a brief description of the research undertaken at Stirling not only in Mathematics but also in several areas of application.
Mathematics & Statistics
Research in the Mathematics and Statistics group is concentrated in three areas: algebraic graph theory, artificial neural networks, and modelling in the social sciences. Algebraic graph theory was the subject of an ICMS workshop in July 1993, devoted to the relation between the structure of a network graph and its algebraic invariants. The Department's work in this area is carried out in collaboration with mathematicians from the University of Belgrade. The work in neural networks is concerned with improved measures of the generalisational ability of a network, and makes use of the KSRI parallel supercomputer at Manchester. The System Modelling and Research group, set up jointly with management scientists, applies modern control theory to system dynamics and undertakes research in the design of organizational structures. Work also continues on energy and environment models relevant to the economics of developing countries.
Centre for Cognitive and Computational Neuroscience (CCCN)
The research of the centre is focused on aspects of vision such as object recognition and the visual processing of images of natural texture, facial gestures and pages of text. A recently introduced area of research is concerned with sound and learning, in particular the perception of simple melodies. The centre is a joint venture of the Departments of Computing Science and Psychology, where the Human-Computer Interface is another topic of common interest.
Computing Science
Here much of the work is in the general area of software engineering. Specific topics include: the specification and verification of quality of service in telecommunication networks; the formalisation of architectural concepts and standards in open distributed processing; techniques and uses of the formal language LOTOS; object-oriented analysis and design; the PICT tool for constructive type theory; garbage collection in functional programming; algebraic methods for complex software systems; and software architectures for a knowledge-based system with heterogenous knowledge sources.Work undertaken in conjunction with CCCN includes: a neurobiologically-based technique for low-level data-driven sound segmentation; the use of multiple phase oscillation in representing data in a neural network; the use of neural networks in processing data indicating driver-tiredness; and an investigation of the levels of accuracy required during training and testing of a neural network.
Natural Sciences
Among the many research activities of the School of Natural Sciences, those with a mathematical or statistical flavour include projects concerned with the ecology of tropical forests, the effects of effluent treatment on the Forth Estuary, the effects of temperature change on marine organisms, the analysis of hydrological and hydrochemical data, climatic variability, ecological and geomorphological change, and the investigation of spatial variability using geostatistical techniques. Also addressed are problems in quantum optics, atomic physics and Fourier transform spectroscopy.
Social Sciences
Several members of the Department of Accountancy and Finance participated in last year's ICMS meeting on Mathematics in Finance. Their interests include non-linear patterns in stock market indices, option pricing, and models of volatility clustering in financial markets.
In the Department of Economics, research topics include a new type of estimator for panel datasets, a model for foreign direct investment, and environmental valuation techniques such as contingent valuation.
James Clerk Maxwell was born in Edinburgh at 14 India Street, a house built for his father in that part of Edinburgh's elegant Georgian New Town which was built after the Napoleonic Wars. Although the family moved to their estate at Glenlair, near Dumfries, shortly afterwards, James returned to Edinburgh to attend school at The Edinburgh Academy. He continued his education at the Universities of Edinburgh and Cambridge. In 1856, at the early age of 25, he became Professor of Physics at Marischal College, Aberdeen. From there he moved first to King's College, London, and then, in 1871, to the distinguished Chair of Experimental Physics at Cambridge where he directed the Cavendish Laboratory. It was at the Cavendish, over the next fifty years, that so much of the physics of today continued to develop from Maxwell's inspiration.
The Impact of Maxwell's Work
James Clerk Maxwell was one of the greatest scientists who have ever lived. To him we owe arguably the most significant discovery of our age - the theory of electromagnetism. He is acclaimed as the father of modern physics and also made fundamental contributions to mathematics, astronomy and engineering.
So much of our technology in the world today stems from his grasp of basic principles of the universe. Wide ranging developments in the field of electricity and electronics, including radio, television, radar and communications, derive from Maxwell's discovery - which was not a synthesis of what was known before, but rather a fundamental change in concept that departed from Newton's view and was to influence greatly the modern scientific and industrial revolution.
Communications: In the early nineteenth century, despite many individual advances in knowledge, there was no linking of a comprehensive theory of electricity and magnetism. In developing this, Maxwell pointed the way to the existence of the spectrum of electromagnetic radiation. Defining fields as a tension in the medium, he stated his belief in a new concept - that energy resides in fields as well as in bodies. This pointed the way to the application of electromagnetic radiation for such present-day uses as radio, television, radar, microwaves and thermal imaging.
Thermodynamics: Maxwell made fundamental contributions to the development of thermodynamics. He was also the founder of the kinetic theory of gases. This theory provided the new subject of statistical physics, linking thermodynamics and mechanics, and is still widely used as a model for rarified gases and plasmas.
Rheology: This is concerned with the investigation and interpretation of the flow behaviour of substances. It has many roles, extending to quality control, across industry (including the food industry) and in medicine. It can be traced back directly to Maxwell's pioneering theoretical and experimental work on topics, such as viscosity, which are strongly dependent on the molecular structure of free-flowing substances.
Engineering: Maxwell was the first to show how to calculate stresses in framed arch and suspension bridges. He also led the work of the British Association committee which defined most of the electrical units in use today; in the associated experiments he pioneered the use of feedback control.
Mathematics: His particular gift was the ability to see phenomena in terms of relationships which could be defined by equations, if necessary abandoning a physical analogy. He invested the term "curl" for the vector operator that appears in his equations for the electromagnetic field.
Nuclear Energy: Calculating the speed of electromagnetic waves, Maxwell postulated that light is a form of electromagnetic radiation exerting pressure and carrying momentum. This provided the basis for Einstein's work on relativity from which the relationship between energy, mass and velocity contributed to the theory underlying the development of atomic energy.
Space Exploration: The discovery of electromagnetic radiation led to the development of radio and infra-red telescopes, currently exploring the farthest reaches of space. His brilliant theoretical study of Saturn's rings provided a physical explanation, recently confirmed by a space probe vehicle.
Photography: Maxwell's many interests included colour. He analysed the phenomenon of colour perception, which led him to invent the trichromatic process. Using red, yellow and blue filters, he produced the first colour photograph - of a Scottish tartan ribbon. This process was the forerunner of today's modern colour photography.
"From a long view of the history of mankind - seen from, say, ten thousand years from now - there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics."
Richard P. Feynman, Nobel Laureate
1990 by Edinburgh University, Heriot-Watt University, International Centre for Theoretical Physics, City of Edinburgh District Council, Lothian Regional Council, Scottish Development Agency.
Aims:
- to create an environment in which the mathematical sciences will develop in new directions.
- to encourage and exploit those areas of mathematics that are of relevance to other sciences, industry and commerce.
- to promote international collaboration, with particular reference to mathematicians working in developing countries.
Activities:
- Research programmes and workshops, aimed at stimulating the chosen topic by bringing together researchers with different backgrounds and different perspectives, who might otherwise not have the opportunity to work together.
- Courses of various types for wide audiences, including courses for post graduates, and courses aimed at participants from industry and commerce. Participation by mathematicians from the developing world is particularly welcomed.
Management Structure:
The overall strategic planning of ICMS is the responsibility of the Steering Committee. For matters of detail the Steering Committee acts through an Executive Committee. Scientific Policy is decided by a distinguished Scientific Advisory Board.
Finally, in planning the scientific programme of the ICMS the Executive Committee is advised by a Programme Committee chosen so as to reflect a broad spread of mathematical interest.
The Scientific Director is Professor A J Macintyre. The day to day running of ICMS is in the hands of the Executive Director, Ms Lucy Young, and an administrative assistant, Miss Louise Williamson.
Steering Committee:
Chairman: Prof J M Howie (Edinburgh Math. Soc.) The Principal of Edinburgh University, The Principal of Heriot-Watt University, The Director of the International Centre for Theoretical Physics Trieste, Prof A J Macintyre (Scientific Director), Councillor George Kerevan (City of Edinburgh District Council), Lord Balfour of Burleigh (Royal Society of Edinburgh), Prof N J Hitchin (London Mathematical Society), Prof E G Rees (Edinburgh University), Prof J M Ball (Heriot-Watt University), Prof M S Narasimhan (Mathematics Section, ICTP), Dr P G Wakely, Prof A J Forty.
Executive Committee:
Chairman: Prof E G Rees (Edinburgh University) Prof J M Ball (Heriot-Watt University), Prof R J Knops (Vice Principal, Heriot-Watt University), Professor A J Macintyre (Scientific Director), Prof G S Boulton (Dean of the Faculty of Science and Engineering, Edinburgh University), Mr I J Wall (City of Edinburgh District Council), Ms Lucy Young (Executive Director).
Scientific Advisory Board:
Prof E B Dynkin (Cornell, USA), Prof M Gromov (IHES, Bures-sur-Yvette, France), Prof P D Lax (Courant Institute, USA), Prof J-L Lions (College de France), Prof J Palis (Rio de Janeiro, Brazil), Prof D Quillen (Oxford), Prof H Weinberger (Minnesota, USA).
Programme Committee:
Chairman: Prof J E Marsden (Berkeley) Prof J Carr (Heriot-Watt University), Prof J M Ball (Heriot-Watt University), Dr P Rowlinson (University of Stirling), Prof M S Narasimhan (ICTP, Trieste), Prof J Coates (Cambridge, LMS), Prof S K Donaldson (Oxford, LMS), Prof J T Stuart (Imperial College, SERC), Prof J M Ball (Heriot-Watt University), Prof E G Rees (Edinburgh University), Prof M Titterington (Glasgow, EMS), Prof R Fletcher (Dundee).
International Centre for Mathematical Sciences 14 India Street EDINBURGH EH3 6EZ
Tel: 0131 220 1777 Fax: 0131 220 1053 e-mail:icms@ maths.ed.ac.uk