Cyril Letrouit of the Laboratoire de Mathématiques d'Orsay presents joint work with Charles Bordenave and Mostafa Sabri on quantum ergodicity and quantum weak mixing for sequences of finite Schreier graphs. The talk, given at the Institute for Advanced Study's analysis and mathematical physics seminar, focuses on graphs that converge in the Benjamini-Schramm sense to an infinite Cayley graph whose adjacency operator has absolutely continuous spectrum. Letrouit walks through a new approach to proving quantum ergodicity on graphs, built from trace computations, resolvent approximations, and representation theory, rather than the spectral methods typically used in this area. The audience is specialists in spectral graph theory and mathematical physics, and the talk assumes familiarity with operator theory and graph limits. It runs just over an hour and sits squarely in current research on how eigenfunctions spread out, or fail to, on large discrete structures as they approach an infinite limit graph.