In the past few years the notion of `strong convergence' of multi-matrix models has found applications across pure mathematics including to random graphs, operator algebras (in several ways), spectral theory of hyperbolic manifolds, and the theory of minimal surfaces.
I will define strong convergence of unitary representations of groups and then discuss the still-mysterious and broad-ranging question of which discrete groups have finite dimensional unitary or 'permutation' representations that strongly converge to their regular representation.
Based on joint works with W. Hide, L. Louder, D. Puder, M. de la Salle, J. Thomas, R. van Handel.
