Integrable systems play an important role in both mathematics and mathematical physics.
Thanks to a particularly rich structure, powerful algebraic and combinatorial methods
combine to yield explicit solutions.
As the number of degrees of freedom in the model tends to infinity, these explicit solutions
allow for a detailed analysis of their properties and reveal surprising universal behaviours.
Prominent examples of integrable systems come from lattice models and random matrices.
The integrable structure has been crucial in analyzing critical phenomena in models such as
the two-dimensional Ising model, a classical model of ferromagnetism still very actively
studied. Similar structures arise in the analysis of eigenvalues of random matrices.
The main mathematical tools come from group theory, special functions and orthogonal
polynomials, and asymptotic analysis.
This project combines the strengths of three Belgian research teams in this direction. It
focuses on current problems that relate to random matrices, lattice models, orthogonal
polynomials and special functions.