On Solving (q,t)-Deformed Matrix Models

I will focus on a class of matrix models arising from supersymmetric localization of three-dimensional supersymmetric gauge theories. They provide natural (q,t)-deformations of classical matrix ensembles such as the Gaussian model, the Laguerre model, and Selberg integrals. I will explain how to establish superintegrability—special averages of Macdonald polynomials—in these models. A key role in the proof is played by the quantum toroidal algebra, which governs the symmetry of these models.