Explore the concept of non-almost finite actions on the Cantor set in this 30-minute conference talk by Matthieu Joseph. Delve into the world of measured group theory as Joseph introduces and examines almost finiteness, a topological analogue of the Ornstein-Weiss tower theorem in measurable dynamics. Learn about the existence of amenable wreath products that admit minimal non-almost finite actions on the Cantor set. Gain insights into this complex mathematical topic, presented as part of the Théories des groups mesurée/Measured Group Theory conference held at the Centre de recherches mathématiques (CRM) in March 2023.