Issue No 11


Workshop Classical and Quantum Integrable Systems and their Symmetries
2–8 December 2001

Scientific Organising Committee:
Ed Corrigan (York),
Chris Eilbeck (Heriot-Watt),
Tetsuji Miwa (Kyoto),
Robert Weston (Heriot-Watt)

Supported by:
The Engineering and Physical Sciences Research Council and the Isaac Newton Institute for the Mathematical Sciences

This workshop was a satellite of the Isaac Newton Institute programme on Integrable Systems, running from July to December 2001.

The emphasis of the ICMS workshop was primarily on quantum integrable systems and the symmetry approach. One objective of the meeting was to foster closer links between the rather separated quantum and classical integrable systems communities. Several of the key advances in recent years have come from individuals and groups that straddle this divide, and it was one of our aims to bring the two communities together and to encourage such work. We also hoped to involve speakers and participants from other fields such as condensed matter theory and string theory.

One of the current endeavours of the Isaac Newton Institute is to try and bring the benefits of its programmes to the wider UK community. This, and the excellent facilities and organisational skills provided by the International Centre for Mathematical Sciences (ICMS) in Edinburgh were the main reasons for choosing to run this meeting as a satellite workshop in Edinburgh. We also strove to involve as many UK people as possible, and to encourage and provide the time for young people to talk.

Almost 70 people took part in this lively meeting held on the Heriot-Watt campus on the outskirts of Edinburgh. Of these around half were based in the UK, and we also had a healthy contingent from other European countries, and from Japan, North America and Russia. Of the 34 talks, 24 were 45 minutes long and were delivered mostly by invited speakers. We took the decision to reserve the remaining 10 shorter slots for younger participants. This was the first time several of these younger participants had given a presentation at a major meeting. We feel that this arrangement worked well, and was very effective in bringing new faces and new ideas into the meeting.

Many of the main talks presented important new results. For example: Cardy presented new exact results for critical scaling functions for self-avoiding polygons. He related this problem first to branched polymers and then to the zero-dimensional Yang-Lee edge singularity. The resulting scaling function is expressed in terms of Airy functions. Such functions also occur naturally in supersymmetry and elsewhere, and many participants were interested in possible parallels in these areas of Cardy’s reasoning.

McCoy presented recent work in which he and his collaborators have discovered that the 6-vertex model at roots of unity has a hitherto unexpected sl2 loop symmetry. Apart from the Ising model, the 6-vertex model is probably the most studied of all solvable lattice models. It is remarkable that a fundamental new symmetry has only recently been found. McCoy presented this work and described the connection between sl2 loop algebra highest weight states and Bethe vectors.

Smirnov talked about the separation of variables approach for a class of quantum integrable models. He presented recent important advances in his ongoing programme to construct a more algebraic-geometrical description of quantum integrable systems.

Shiraishi described a recent breakthrough that has enabled him to construct, after 10 years of labour, a free-field realisation of the infinite-dimensional algebra associated with the 8-vertex model. Such a construction completes the ‘algebraic analysis’ picture of this model, and permits a direct computation of exact correlation functions.

There were also many impressive short talks by the younger participants. The presentations by Caux, Castro-Alvaredo and Doikou noticeably inspired many scientific conversations.

Generally, there was a great deal of lively interaction between participants at the meeting. This was encouraged both by the frequent pauses in the schedule and probably by the geographical isolation of the Heriot-Watt campus. Several collaborations certainly grew out of these discussions, for example, following Nepomechie’s talk and subsequent conversations, he and Delius are now working together on the construction of solutions of the boundary Yang-Baxter equation.

Another very positive aspect of the meeting was the involvement of a substantial number of young Japanese participants. This was the first time that several of these participants had visited the UK. Both the UK and Japan have traditionally been very strong in this field, and we anticipate that the meeting will have helped establish further lasting connections between these two communities.

We were indeed fortunate in attracting many of the world’s experts in the field, and the range of interests of our participants and topics presented was unusually wide – much broader than most of the specialised conferences in either classical or quantum integrable systems. The examples of talks given above demonstrate that interesting and important new results were discussed, and we hope and anticipate that the meeting will have advanced research in the field. We believe that this will have a lasting effect on the health of mathematical physics in the UK.

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Agafonov, Serguei – Loughborough University
Arnaudon, Daniel – LAPTH, CNRS Avan, Jean – LPTHE Paris VI/VII
Bogdanov, Leonid – Landau Inst for Theoretical Physics
Braden, Harry – University of Edinburgh
Brezhnev, Yurii – Heriot-Watt University
Buchstaber, Victor M – Steklov Inst. of Mathematics
Bullough, Robin – UMIST
Cardy, John – Oxford University
Carr, Sam – Brookhaven National Lab
Castro-Alvaredo, Olalla – Freie Universitat Berlin
Caux, Jean-Sebastien – Oxford University
Chalykh, Oleg – Loughborough University
Corrigan, Edward F – University of Durham
Crampe, Nicolas – LAPTH
Delius, Gustav W – University of York
Doikou, Anastasia – University of York
Dorey, Patrick – Durham University
Eilbeck, Chris – Heriot-Watt University
Enolskii, Victor – Heriot-Watt University
Evans, Jonathan Mark – University of Cambridge
Fairlie, David – University of Durham
Fateev, Vladimir – LPM University Montpellier II
Feher, Laszlo – University of Szeged
Feigin, Misha – Loughborough University
Feigin, B L – Landau Instititute
Fioravanti, Davide – University of Durham
Flaschka, Hermann – University of Arizona
Fokas, Thanasis – Imperial College
Frappat, Luc – LAPTH
Grava, Tamara – Imperial College
Inoue Yamazaki, Rei – University of Tokyo
Johnston, Des – Heriot-Watt University
Kedem, Rinat – University of Illinois
Konno, Hitoshi – Hiroshima University
Kuznetsov, Vadim – University of Leeds
MacKay, Niall – University of York
Maillet, Jean-Michel – ENS Lyon
Mathieu, Pierre – Université Laval
McCoy, Barry – State University of New York
Mikhailov, A V – University of Leeds
Miwa, Tetsuji – Kyoto University
Nazarov, Maxim – University of York
Nepomechie, Rafael – University of Miami
O’Donnell, Peter – Anglia Polytechnic University
Odake, Satoru – Shinshu University
Ohyama, Yousuke – Osaka University
Pelloni, Beatrice – University of Reading
Ragnisco, Orlando – University of Roma Tre
Ravanini, Francesco – University of Bologna
Rittenberg, Vladimir – Bonn University
Rossi, Marco – Heriot Watt University
Sanders, Jan – Vrije Universiteit Amsterdam
Sasaki, Ryu – Yukawa Institute for Theoretical Physics
Schroers, Bernd – Heriot-Watt University
Shiraishi, Jun’ichi – University of Tokyo
Sklyanin, Evgueni K – University of York
Smirnov, Fedor – University of Paris-Jussieu
Takebe, Takashi – Ochanomizu University
Takemura, Kouichi – Yokohama City University
Taormina, Anne – University of Durham
Tateo, Roberto – University of Durham
Wang, Jing Ping – Vrije Universiteit Amsterdam
Watts, Gerard – King’s College, London
Weston, Robert – Heriot-Watt University
Zakharov, Vladimir – Landau Institute
Zambon, Cristina – The University of York
Zyskin, Maxim – Oxford University

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