Classical and Quantum Integrable Models

London Mathematical Society and EPSRC Short Instructional Course

July 19 2010 - July 23 2010

The problem of integrating differential equations goes back to the origins of calculus and Newton's development of mechanics. Although certain simple models in classical mechanics, like the Kepler problem, were found to be integrable from the outset, Poincaré's discovery of chaos in the three-body problem led to the realization that integrable cases of dynamics are the exception, rather than the rule.

The importance of integrable systems began to be recognized again in the twentieth century. The analysis of stable solutions of a nonlinear partial differential equation modelling shallow water waves, led to the discovery of the inverse scatting method for solving integrable PDEs. At around about the same time, exact scattering states were found to occur in certain quantum field theories. Meanwhile, Painlevé's differential equations resurfaced in the description of scaling behaviour for crticial phenomena in statistical mechanics.

As well as providing a new set of basic tools in mathematical physics, the theory of integrable systems was found to have deep connections with many different areas of pure mathematics: Hamiltonian mechanics and the explicit description of abelian varieties in algebraic geometry; Toda field theory and harmonic maps in differential geometry; r-matrices and the Yang-Baxer equation in quantum groups.

The school will introduce the main concepts and methods in integrable systems and some current research areas where these methods are being further developed and applied. The school will also be accessible to beginning graduate students in theoretical physics who require techniques for exactly solvable models.

Lecture courses

There will be three lecture courses:

  • Quantum integrable systems Anastasia Doikou (Patras)
  • Hamiltonian approach to integrable discretzation Yuri Suris (TU Berlin)
  • Classical and quantum integrable systems Evgeni Sklyanin (York)

The lectures will be supported by examples classes tutored by Ian Marshall, Matteo Petrera and Pavlos Xenitidis and there will be guest lectures by Ed Corrigan (Durham), Masatoshi Noumi (Kobe) and Jenya Ferapontov (Loughborough).

An outline of the lectures can be downloaded here.


The school will run from Sunday 18 July (arrival) to Friday 23 July. A timetable is available here.

Accommodation has been arranged in Rutherford College on campus. Breakfast will be in Rutherford dining hall between 8am and 9am. If you arrive after Rutherford Reception has closed, please call Campus Watch using the intercom system, or go direct to their office (open 24 hours) by the banks Natwest and Barclays.
Check in: after 2pm on Sunday 18th July
Check out:before 10am on Friday 23rd July

Internet access will be available. Instructions for connecting to the wireless on campus or finding a PC are here. We will provide details of the conference IT account at registration.

List of participants.

Some photographs of the banquet and Whitstable taken by Efstathios Charalampidis.


Canterbury is approximately one hour by train from London St Pancras or two hours twenty minutes from Paris (via Ashford International). Travel information is available here.


  • All research students registered at a UK university will be charged a registration fee of £ 100 (in the case of EPSRC funded research students, this fee should be paid by their departments from their Doctoral Training Account, for non-EPSRC research students, their department might be prepared to pay the fee). They will not be charged for subsistence costs.
  • UK-based postdocs will be charged a registration fee of £ 100, plus half the subsistence costs (£ 140), £ 240 in total.
  • All others (overseas students and postdocs, those working in industry) will be charged a registration fee of £ 250 plus the full subsistence costs (£ 280), £ 530 in total.

All participants must pay their own travel costs (for EPSRC funded students, this should be covered by their DTA). Fees are not payable until a place on the course is offered. In the event of over-subscription preference will be given to UK-based research students.


Please go to the LMS page to register. Registration closes on 28th May 2010.

SMSAS Bursaries

The School of Mathematics, Statistics and Actuarial Science has a number of small bursaries available to assist some overseas research students to attend the course. If you wish to apply for a bursary, you should send a brief CV to the local organisers. Please also briefly explain how you will benefit from attending the course, the total costs for you to attend the school and what funding you have applied for or expect to receive from other sources. You must also register with the LMS by the closing date.


Please contact the local organisers if you have any questions.

Local Organisers

Clare Dunning, Andy Hone and Jing Ping Wang.

Supported by