Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Explore the theory of uniqueness and non-uniqueness of infinite clusters for percolation on groups in this 49-minute conference talk by Tom Hutchcroft. Delivered as part of the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), the presentation surveys both classical results and ongoing developments in the field. Gain insights into the connections between percolation theory and group-theoretic concepts such as amenability, hyperbolicity, property (T), and L^2 Betti numbers. Delve into this advanced mathematical topic and its applications in geometric and asymptotic group theory.