The LMS-EPSRC Durham Research Symposia began in 1974, and form an established series of international research meetings, with over 100 symposia to date. They provide an excellent opportunity to explore an area of research in depth, to learn of new developments, and to instigate links between different branches. The format is designed to allow substantial time for interaction and research. The meetings are held in July and August, usually lasting for 10 days, with up to 70 participants, roughly half of whom will come from the UK. Lectures and seminars take place in the Department of Mathematical Sciences, Durham University.

Summer School Speakers (26-27 July)

• Mark Ablowitz (Colorado): Inverse scattering transform: history, background and methods
• Alexander Bobenko (Berlin): Integrability in discrete differential geometry
• Robert Bryant (Duke): Integration techniques for exterior differential systems
• Franco Magri (Milano): Bi-Hamiltonian formalism
• Alexander Mikhailov (Leeds): Symmetry approach to integrability
• Alexander Veselov (Loughborough): Integrability: historical overview
• Richard Ward (Durham): Twistor theory and integrability

Registered conference participants (28 July - 4 August)

The history of integrable systems goes back to 19th century work in classical mechanics, differential geometry, complex analysis, differential equations and nonlinear special functions. The modern theory is grew up around the study of KdV type equations, following the discovery of multi-soliton solutions, infinite number of conservation laws and the Inverse Scattering Transform in the 1960s and 1970s. In the 1980s new ideas came via integrable field theories and connections with harmonic maps and differential geometry were re-established. Links with other areas of mathematics - algebraic geometry, twistor theory, self-duality, representation theory, number theory, enumerative geometry, Gromov-Witten theory and Topological Quantum Field Theories grew in the 1990s and through into the 21st Century.

The aim of the Symposium is to bring together leading international researchers in the various sub-fields of integrable systems, concentrating primarily on the mathematical aspects of the theory.

The inverse scattering transform (IST) is a method to solve the Cauchy problem associated with a class of nonlinear evolution equations. The lectures will give some history and background. The associated linear systems and methodology will be outlined for some physically significant equations such as the Korteweg-deVries (KdV), nonlinear Schrodinger (NLS), modified KdV (mKdV), and sine-Gordon equations. The recently discovered symmetry leading to the integrable nonlocal NLS equation and its IST will also be mentioned.

(under construction)

Contact: If you are interested, please email ma.gaai16@durham.ac.uk

Useful information about travelling to Durham can be found on the Department of Mathematical Sciences and Durham University webpages.

Accommodation for participants will be in Grey College. Guest rooms offer en-suite and internet facilities. Attendance is by invitation only and fees for self-supporting participants are payable by cash, credit card, sterling cheques or sterling travellers cheques at registration.