### 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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**Participants:** 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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