**
INTERNATIONAL ASSOCIATION OF MATHEMATICAL PHYSICS
**

**IAMP NEWS BULLETIN
**

**December 1997
**

President

Prof. E. H. Lieb

Jadwin Hall

Princeton University

Princeton, NJ 08544-0708

USA

Vice-President

Prof. H. Araki

Department of Mathematics

Faculty of Science and Technology

Science University of Tokyo

Yamazaki 2641 Noda-shi

Chiba-ken 278

JAPAN

Secretary

Prof. C. Radin

Mathematics Department

University of Texas

Austin, TX 78712

USA

Treasurer

Prof. S.R.S. Varadhan

Courant Institute

NYU

251 Mercer Street

New York NY 10012

USA

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** PRESIDENT'S REPORT**

It is customary for the IAMP president to report on events of interest to the Association and to mathematical physics generally. This time, the main interest centers on our triannual meeting that was held this summer in Brisbane and it is no exaggeration to say that it was hugely successful. The organization by our hosts was among the smoothest I have seen at any large meeting anywhere, and on behalf of IAMP I would like to say how grateful we are.

The local organizing committee that carried this out consisted of Tony Bracken (chair), Mark Gould (secretary), Barry Jones (treasurer) and many others. The International Scientific Advisory Committee together with the Australian Scientific Committee gave us a scientific program that brought out clearly that mathematical physics, as a field in its own right, is alive and well and is also adaptable to the changing currents in physics and mathematics. That is to say, the traditional subjects that have guided this Association since its founding are vibrant, but we were also treated to some new foci that should continue with us for some time.

Several items concerned with this meeting are to be found in this issue of the News Bulletin. Tony Bracken has kindly contributed a synopsis of the meeting. My brief opening remarks are also included, partly because they mention the people who made it all work and partly because they contain some historical remarks that younger members might not know about.

One of the decisions by the Executive Committee in Brisbane was that the next Congress, to be held in 2000, will be in London. A welcoming message by Boguslaw Zegarlinski, the chair of the local organizing committee, will be found in this issue.

Until then, let me hope that we may have many small local and/or topical meetings, and I would encourage everyone to think about organizing such meetings. They can be quite useful in bringing the community together.

The Association is financially healthy and we are trying hard to find ways in which we can be useful to the members. One way is to provide a web page

http://www.ma.utexas.edu/iamp/index.html

maintained by Charles Radin and on which this News Bulletin will be stored. In fact, it is hoped, eventually, to have the News Bulletin exclusively electronic, i.e., to eliminate the hard-copy and its costs and distribution problems. At the Executive Committee meeting in Brisbane it was determined that this would be the last hard-copy of the bulletin with full distribution.

* The News Bulletin will henceforth be sent by email to all those
members for whom we have an email address. If you want to have a
hard-copy bulletin, you must request it from the secretary.*

After reviewing these results, further action may be taken restricting hard copy distribution.

As you can see from this, it is very important that we have your email address and that you keep it up-to-date. The person to send it to is the treasurer, Raghu Varadhan, at

Another way in which we can make IAMP more useful is to have a section
on our web page devoted to * Open Problems.* Michael Aizenman has
kindly agreed to edit this section and an announcement, with some more
details, is included in this issue.

*(Note added: See
*
http://www.ma.utexas.edu/iamp/probs.html
* for the details.)*

There is also a message from Eugene Wayne, the chair of our Committee on Electronic Communication. Ideas in this area are most welcome.

One of the really pleasurable events in the General Assembly in Brisbane was the award of three prizes in Mathematical Physics established by Daniel Iagolnitzer. This was also a good year for the recognition of Mathematical Physics in terms of several other prizes, as mentioned later.

The officers of the Association have changed. Daniel Iagolnitzer resigned as treasurer in June. It was not possible to find a replacement during the summer, but in September Raghu Varadhan kindly agreed to assume this responsibility. The other officers remain as before: Huzihiro Araki is Vice-president and Charles Radin is Secretary.

We have three new Associate members, and I should like to welcome them and thank them for their support. They are Kluwer Academic Publishers, Microsoft and the Max Planck Institute for Mathematics in the Sciences, Leipzig.

Elliott Lieb, December, 1997

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** SECRETARY'S REPORT**

This is the last paper News Bulletin which will be distributed to our full membership; in future, all members will periodically receive by email a snapshot of the information currently on our web site together with appropriate timely announcements. (Those who wish to also receive the next snapshot in paper form should contact me.)

The reasons for the switch to electronic communication are two-fold -- the large savings in expense for reproduction and distribution, and, more significantly, the enhanced service available through the web. Examples of the latter already in place include the membership data, the extensive and timely preprint archives, and the current and detailed information about conferences now possible through web links.

In conclusion I urge you to check out our web site:

http://www.ma.utexas.edu/iamp/index.html

or the mirror site:

http://mpej.unige.ch/iamp/index.html

In particular, please check that the information listed for you on the membership list is accurate and complete, especially the email address. Amendments are easily done through the web; alternatively, please send the information to the treasurer: S.R.S. Varadhan, varadhan@cims.nyu.edu. And while you are at it, check your dues status and bring it up to date if necessary. (This can also be checked from the address label on this bulletin.)

Charles Radin, Secretary of IAMP (iamp@math.utexas.edu)

** REPORT FROM THE IAMP COMMITTEE**
** ON ELECTRONIC COMMUNICATION**

The IAMP now has an active site on the World Wide Web, located at ``http://rene.ma.utexas.edu/iamp''. The site is maintained by the Association Secretary Charles Radin, and contains a host of useful information including the Association's membership list, the Bulletin, and links to other mathematical physics sites.

There is a mirror of this web site in Geneva (http://mpej.unige.ch/iamp/index.html) which should provide faster response times for European users. It would also be nice if we could establish a mirror site in Asia or Australia. If anyone is willing to volunteer to establish and maintain such a site, or if you have any other suggestions for ways in which the Association could improve the electronic services it provides to its membership, please contact the IAMP Committee on Electronic Communication, care of Eugene Wayne ( cew@math.bu.edu )

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** XIII International Congress of
Mathematical Physics**

17 - 22 July 2000, Imperial College, London, UK

Dear Colleagues,

Through an interesting and fortunate arrangement made in the history of the IAMP ten years ago, the next International Congress of Mathematical Physics will take place in the millennium year. It will be a special year in many respects: through activity both on the Earth and on the Sun.

We are very pleased that during the millennium year, between 17th and 22nd July, we will host the XIIIth International Congress of Mathematical Physics at Imperial College, London. It will again be an opportunity for meeting colleagues, for presenting excellent recent results and for fruitful scientific discussions. But also at this special moment in time it will be a good opportunity to look back and summarize the achievements made in this century in the area of Mathematical Physics. Certainly every speaker will wish to tell us about great open problems. We also plan to have a number of round-table discussions which will help us to create a vision of the most important directions for the future.

It will be important during this particular Congress to underline relevance of the mathematical and physical research for modern society. Therefore we plan to have an extensive public programme consisting of a number of open lectures which we hope will also be intellectually enjoyable to all participants of the Congress.

Travelling to a congress from other countries takes time and costs money. Fortunately London has a superb location in respect of travel costs as well as convenience of travel connections. With a large number of tourist and other attractions it is also a very interesting place to visit.

To make your trip even more worth your while we will have a number of satellite meetings organized by UK enthusiasts:

- Bristol: PDEs and Schrödinger Operators
- Cambridge: Statistical Mechanics and Related Fields
- Edinburgh: Dynamical Systems
- Nottingham: Noncommutativity, geometry and probability
- King's College London: Disordered Systems
- King's College London: Quantum Groups and Integrable Systems
- Queen Mary and Westfield College London: Strings and Gravity
- Oxford: Bio-Math-Phys
- Warwick: Stochastic Analysis on Loop Spaces
- Imperial College: Kindergarten - Special Programme for Post Graduate Students.

We will make every effort to keep the conference fee at a very low level and to organize a possibly large support fund for attendees. We are also able to provide a large amount of inexpensive accommodation.

Detailed information will be available under the following Internet address: http://icmp2000.ma.ic.ac.uk/

For communication the following e-mail address can also be used: icmp2000@ic.ac.uk

We very much hope that by your active participation you will make this Congress special and memorable. For good planning please make a note in your diary now and come in the year 2000.

On behalf of the Local Organizing Committee I am pleased to send you this very warm invitation.

Yours sincerely,

Boguslaw Zegarlinski Chairman of the Local Organizing Committee ICMP2000

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**
Report on the Congress in Brisbane**

July 13 to July 19, 1997

The ** XIIth International Congress** was held from July 13 to 19 on the
campus of the University of Queensland in Brisbane. It was attended
by 346 delegates.

There were 13 one-hour plenary lectures, presented by R Bartnik, R Baxter, J Feldman, S Ferrara, G Gallavotti, G 't Hooft, V Jones, V Kac, M Loss, M Mezard, P Sarnak, H-T Yau and L-S Young.

There were 9 two-hour invitational sessions, with the themes

- disordered systems
- general quantum field theory
- general relativity & string theory
- integrable models
- operator algebras
- quantum chaos & semiclassical limit
- quantum mechanics
- statistical hydrodynamics
- statistical mechanics

in which 35 shorter, invited talks were given.

And there were 107 short, contributed talks plus 79 posters presented.

All of this was fitted into 6 mornings and 4 afternoons, and was supplemented by a busy social program in the evenings and on the midweek Wednesday afternoon, when there was a tour to view local fauna and flora. A novel feature of the social program was a concert by the resident University of Queensland chamber ensemble, at which a short composition specially commissioned for the Congress, and sponsored by the Australia Council for the Arts, had its premiere.

The General Assembly, held on the Wednesday evening, had some very lively discussion about directions, new and old, in mathematical physics. IAMP President Elliott Lieb also awarded three prizes during the Assembly. Vaughan Jones gave a very successful public lecture on the Friday evening.

Many delegates also took the opportunity to attend one or more of the several other conferences in the Asia/Pacific region which were loosely associated with the Congress, and which were held in the weeks before or after the Brisbane meeting.

The Congress was blessed with fine weather and good luck. There were no major problems with the program or the accommodation arrangements, and delegates seemed to enjoy the meeting. Most important for the IAMP, the Congress was a financial success, and the organizers have been able to refund all the money advanced by the IAMP, plus the registration surcharges paid by 113 non(financial)members who attended.

Thanks to all those who helped with the organization - far too many to list here, but special thanks to the Local Organizing Committee, and to a great bunch of helpful grad students. Thanks also to our supporters and sponsors, especially IMU and IUPAP, the Australian Mathematical Society, the Universities of Adelaide, Melbourne and Queensland, and the Australian National University.

The contributions of the plenary and invited speakers to the Proceedings have almost all been received, and will go to the publisher shortly. All delegates will receive a copy in due course.

Tony Bracken

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** OPENING REMARKS, Brisbane, July 14 ,1997**

Elliott Lieb

On behalf of the International Association of Mathematical Physics, I welcome you all to this twelfth in the series of International Congresses.

First of all I want to thank, the many people who organized this splendid chance for our community to get together and get to know each other's work.

There is the International Scientific Advisory Committtee chaired by H. Araki, with Tony Bracken, Tom Spencer, Arthur Jaffe, Giovanni Jona-Lasinio and S T Yau.

The Australian Scientific Committee chaired by Angas Hurst, Derek Robinson, Paul Pearce, Bob Delbourgo, Alan Carey, Phil Broadbridge, Gerard Milburn, Peter Jarvis and others.

The Local Organizing Committee in Brisbane: Tony Bracken (chair), Mark Gould (secretary), Barry Jones (treasurer), Jon Links, David de Wit, Yao-Zhong Zhang, Katrina Hibberd, Iain Clark, David MacAnally, Mabo Suzuki, Phil Isaac and Jack Ge.

To the audience I would say that if you have never been involved with something of this dimension then you probably have only a faint idea of the tremendous amount of work involved. In particular, Tony Bracken, who wore three hats has certainly earned a place in our hearts for his tireless efforts.

One of the gifts that the older generation can pass on to the younger is the story of how we got where we are. That story is a bit complicated and involves the realization by some young upstarts in the 1950's and 60's that theoretical physics consisted of more than simple back of the envelope calculations. The enormous success of quantum mechanics in the 30's and 40's had led the major figures in physics to the view that mathematical thought, viewed from the perspective of physical reality, was cerebral calcification.

Bit by bit, the idea that one could actually prove useful theorems about the problems of physics---an early example being the existence of the thermodynamic limit---slowly gained ground. But I must note, parenthetically, as pointed out to me by Jean Bricmont, that some of the most elegant and interesting rigorous results were contributed by card carrying physicists instead of people who made a profession of mathematical physics. But I don't want you to think that this was always the case.

In any event, by 1972 it was felt that there were enough specialists in mathematical physics in the world to have an international conference on the subject. This took place in Moscow. Then in 1974 in Warsaw (in those days the conferences were not so large and expensive and having one every two years was not considered excessive). At the Warsaw meeting, the idea of an Association was explored, and again in Kyoto in 1975. The statutes were assembled and Walter Thirring became the first President in 1976. The first meeting in this series under IAMP auspices was in Rome in 1977. This was followed by Lausanne (1979), Berlin (1981), Boulder (1983), Marseille (1986), Swansea (1988), Leipzig (1991) and Paris (1994).

Finally, after much effort on the part of our hosts we are able to cross the equator and take a different view of the world. I hope there will be more such meetings south of the equator, perhaps in South America. In any event, I wish you all, Australian and overseas participants, a delightful and culturally profitable congress.

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** AWARDS FOR MATHEMATICAL PHYSICISTS IN 1997**

It is a pleasure to announce that several of our colleagues received awards this year for their work in mathematical physics. Such recognition is an encouragement for all of us and we congratulate them on their achievements, so justly recognized.

Three prizes in mathematical physics established by Daniel Iagolnitzer were awarded in the General Assembly of IAMP in Brisbane. The IAMP committee that chose the recipients consisted of Sergio Doplicher (chair), Jürg Frühlich, Daniel Iagolnitzer and Aubrey Truman. The prizes were awarded to Rudolf Haag, Maxim Kontsevich and Arthur Wightman, with the following citations:

* Rudolf Haag:* For his fundamental contributions to the quantum
theory of systems with infinitely many degrees of freedom, as one of the
founders of modern Quantum Field Theory, where he discovered the central
role of the principle of locality and of the concept of local
observables as roots of all the conceptual and formal structures; and as
a leader in the operator algebraic analysis of the foundations of
Quantum Statistical Mechanics. Of all these aspects his recent book is
a superb condensation.

* Maxim Kontsevich:* For his contributions to topological gravity,
establishing a deep link between quantum gravity, string theory and the
geometry of the moduli space of Riemann surfaces; to topological
sigma-models on compact Kaehler manifolds; to mirror symmetry, and for
the notion of quantum deformations of cohomology spaces; for the
contributios to Chern-Simons theories and the construction of knot
invariants; for the discovery of topological string theoretic aspects in
one dimensional dynamical systems.

* Arthur Wightman:* For his central role in the foundations of the
general theory of quantized fields, the powerful impetus impressed
promoting resarch on various aspects of Modern Mathematical Physics (on
constructive QFT, and on domains ranging from statistical mechanics,
dynamical systems and ergodic theory to integrable systems, Schroedinger
Operators and renormalization theory), for his expository contributions
of a masterly level to mathematical physics.

Some other awards:

* Jürg Fröhlich* received the Benoist prize, which is the most
prestigious science prize for Swiss citizens or residents.
The citation (translated) is

For his work on phase transitions, electron localization, and on the theory of the quantized Hall effect.

The Wolf prize in mathematics was awarded this year to Joseph Keller and Iakov Sinai. The citations are

* Joseph Keller:* For his profound and innovative contributions, in
particular to electromagnetic, optical and acoustic wave propagation,
and to fluid, solid, quantum and statistical mechanics.

* Iakov Sinai:* For his fundamental contributions to mathematically
rigorous methods in statistical mechanics and the ergodic theory of
dynamical systems and their applications in physics.

* Michael Aizenman* and * Edward Nelson* were elected to the U.S.
National Academy of Sciences.

Please notify the Secretary, Charles Radin, of 1998 awards.

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The German Max-Planck Society decided to found a Max-Planck Institute for Mathematics in the Sciences in Leipzig. The official opening ceremony took place on October 2, 1996. The new Institute is the second Max-Planck Institute devoted to the mathematical sciences, after the one in Bonn whose founding director was Friedrich Hirzebruch.

The purpose of the Institute is to carry out research in pure and applied mathematics, to foster the dialogue between mathematics and the sciences and to integrate modern scientific advances in the sciences into mathematics. Historic experience shows that problems from physics, chemistry, biology and other sciences have inspired new developments in mathematics while mathematics in turn has had a profound impact on these fields. Fourier's analysis of the heat equation, for example, lead to the development of harmonic analysis, Gauss' work as a surveyor inspired his theory of surfaces and the development of differential geometry which now forms the basis of general relativity and the Standard Model in particle physics, Heisenberg's formulation of quantum mechanics accelerated the development of functional analysis and operator theory, research in nonlinear dynamics was partly motivated by and had a strong impact on celestial mechanics, the theory of compensated compactness partly grew out of problems of the binding of atoms, and gauge field theories have deep connections with topology and geometry.

To foster the exchange of ideas the Institute will have a few permanent positions and a variety of temporary positions for young scientists, as well as an active programme of long and short term visitors. It is planned to build up some research groups that work together on specific projects.

Among the visiting positions there will be a particularly distinguished `Sophus-Lie Visiting Professorship' for which eminent senior scientists will be invited for one or two year terms in order to stimulate the exchange between mathematics and the sciences. The name for this positions has been chosen in honour of the Norwegian mathematician Sophus Lie (1842-1899) who worked in Leipzig from 1886 to 1898 and whose deep theories of symmetry groups and differential equations have had a profound and decisive influence on the development of 20th century theoretical physics.

The main areas of mathematical research will be analysis, geometry and mathematical physics. A prominent theme will be the theory of nonlinear partial differential equations. Specific topics will include Riemannian and algebraic geometry as well as their interaction with modern theoretical physics (harmonic maps, minimal surfaces, Ricci flow, mean curvature flow, Yang-Mills and Seiberg-Witten equations), mathematical models in materials science (microstructure, homogenization, phase transitions, fracture, interfaces and thin films), continuum mechanics (elasticity, fluid and gas dynamics), nonlinear waves and pattern formation, many-particle systems, phenomena in general relativity, quantum field theory, neural networks and models of cognition.

Interaction with the sciences will include a broad spectrum of topics, ranging from fields that already have a strong interaction with mathematics, such as particle physics or continuum mechanics to areas whose mathematization is just beginning, such as cognition or materials science.

To complement analysis and modelling by numerical simulation, it is also planned to build up a research group in scientific computing.

The Institute has started with a board of three directors consisting of Eberhard Zeidler (acting director), Jürgen Jost, and Stefan Müller, with Jürgen Moser as scientific advisor.

Further information can be found on the home page: http://www.mis.mpg.de