About:

This workshop will bring together experts in integrable systems in general, though will focus on three specialised themes:

(i) Regularity and solutions;
(ii) Non-commutativity, both in terms of non-Abelian (eg.\/ matrix) versions of classical integrable systems and in terms of non-commutative independent variables; and
(iii) The connections of such systems to random matrix theory.

The UK has always been at the forefront of, and has a reputation in, integrable systems research. It is an area that glues together topics in mathematical physics, analysis, algebra, geometry, applied mathematics and probability. Research in non-commutative integrable hierarchies has had a recent resurgence - they have many applications, including (eg.) in non-commutative nonlinear optics, and have strong links to string theory. The main themes outlined align with, and will be led, by recent research by the invitees. We propose a different than usual workshop format, along the lines of those held at Oberwolfach and the American Institute of Mathematics. Nominated experts give feeder presentations in their areas on successive mornings, outlining the current frontier of research and open problems. In the afternoons, these are followed up by discussion sessions and working groups who report back to the workshop as a whole at the end of the day. The workshop structure develops dynamically throughout the week. The organisers and the Scientific Advisory Group meet daily to set the agenda ahead, using feedback from the end-of-day reports and participants.

Goals of the Workshop: 
Our goals, and the focus of the workshop, are as follows:

  (1) Provide a platform for researchers in integrable systems to communicate their collective knowledge and interact,
  and in particular, to present the state-of-the-art of what is known;

  (2) Identify, outline and elucidate the links between integrable systems and topics in algebraic geometry (eg. Fay identities),
  algebras of operators (eg. Hankel operators), the regularity of solutions (eg. via Fredholm Grassmannian flows) and random matrix theory (RMT).
  A particular thread throughout will be the generalisation of these connections to the non-commutative setting;

  (3) Work in larger and smaller groups on concrete problems pushing the boundaries and frontiers of knowledge of the themed
  topics identified herein or that naturally arise as the workshop progresses;

  (4) Lay out long-term research themes and strategies with an emphasis on applications. 

Information on particpation to follow in due course.