Integrability has played and plays an important role in condensed matter physics, mathematical physics and more recently string theory. Considerable activity is brewing at the interface of those areas. New insights are emerging on the relation between integrability and conformal field theories through the study of integrable deformations and of holography, especially in AdS(3)/CFT(2). AdS/CFT integrability has also seen remarkable advances in the study of correlation functions, including those involving defects. The techniques employed there are closely connected to the study of finite-volume form factors, and of non-equilibrium dynamics in condensed matter physics. The study of CFT correlators is also part of a broader renewed interest in the conformal bootstrap program to which integrability is poised to contribute, as links are being established between Calogero-Sutherland models and conformal blocks, for example. Finally, new insights have emerged on the very nature of integrable models, as a direct realisation of classical and quantum models from gauge theories casts a new light on them and may provide the right formalism to construct new "RTT" representations of quantum loop algebras.

This rich web of connections is so far only partially explored. Our aim is to put together a critical mass of researchers with complementary expertise from across the mathematical physics, condensed-matter physics and string theory communities in order to unravel it.