Many phenomena in Nature are linear and for this reason are well understood. But even small non-linearities may have profound consequences. Physicists are well familiar with this. All forces in nature ultimately arise from nonlinearities that give rise to interactions among elementary particles. The terms "non-linearities" and "interactions" are synonymous in physics and oftentimes are used interchangeably.

If deviations from linearity are small they can be taken into account with the help of perturbation theory, powerful method that successfully describes a plethora of phenomena ranging from planet motion to high-energy collisions in particle accelerators.

Certain physical phenomena, however, are intrinsically non-linear. When interactions among constituents are strong, they cannot be regarded as small perturbations on top of linear evolution. Quantitative description of non-linear phenomena is always difficult, and many famous unsolved problems in physics remain such because strong non-linearities are involved. The mechanism by which strong interactions keep quarks bound inside hadrons is intrinsically non-linear and is not fully understood to this day. Complete theoretical description of turbulence is still lacking despite its obvious technological importance and more than a century-long efforts.

All this makes solvable models, where non-linearities can be taken into account exactly no matter how strong they are, very valuable. Solvable models often capture essential, universal aspects of non-linear dynamics. A famous example is Onsager's exact solution of the two-dimensional Ising model which played fundamental role in the theory of critical phenomena. Another example is Bethe's exact solution of the Heisenberg model for a chain of interacting atomic spins.

The model studied by Bethe is an example of integrable system sharing with other models in this class plethora of hidden symmetries, that are not obvious from the model's formulation. Additional symmetries enable us to understand integrable models in great detail, and get a full control of highly non-linear, strongly-interacting regime. Integrability has numerous applications in strongly-correlated condensed-matter systems, disordered models far from equilibrium, String Theory and Quantum Gravity. It underlies the theory of solitons and has inspired important developments in pure mathematics.

Current research at Nordita is focussed on subtle relationship between Quantum Field Theory, String Theory and integrable models. Integrability has shed light on the inner working of the AdS/CFT duality that relates gauge interactions with String Theory and quantum gravity. Progress in this area resulted in the first ever exact solution of interacting Quantum Field Theory in 3+1 dimensions, and has potential to boost our understanding of gauge theories that underly our current understanding of fundamental interactions among elementary particles.