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Integrable systems play a major role in many areas of mathematics. The concept of integrability covers any system, classical or quantum, which has sufficiently many conservation laws to allow all physically relevant quantities to be calculated exactly, at least in principle. Such conservation laws are signals of underlying symmetries, but these are often hidden, and it is often a mathematical challenge to uncover them. Traditionally there have been many deep connections with algebra and representation theory, as well as functional analysis and statistical mechanics. In more recent decades, the interplay with topology, knot theory, geometry, and string theory has become extremely prominent, with integrable quantum field theories being at the core of many of these developments. One of the attractions of integrability is that it does not rely on approximations depending on small parameters, and thereby opens the door to regimes of quantum field theory that are otherwise extremely hard to treat. Such non perturbative phenomena are notoriously hard to pin down and continue to inspire mathematical physicists, generation after generation. 

The UK ICFT meetings bring together participants with a broad spectrum of expertise who have contributed significantly to the advances in the field of integrability. They are actively engaged in the mentoring of early career mathematical physicists and the training of PhD students, who benefit from such events through contributing talks or posters and who have an opportunity to integrate and consolidate a thriving community of researchers.

This event is sponsored by the London Mathematical Society under a Scheme 1 Grant.