Gary Froyland School of Mathematics, University of New South Wales Detecting and locating near-optimal almost-invariant sets and cycles Wednesday 10th November 14:05-14:55pm, Carslaw Lecture Theatre 273. Chaotic dynamical systems are often transitive, although this transitivity is sometimes very weak. It is of interest to divide the phase space into large regions, between which there is relatively little communication of trajectories. I will discuss fast, simple algorithms to find such divisions and state relevant convergence results. Our approach uses a blend of modern dynamical systems, graph theory, and reversible Markov chains. An adaptive algorithm is developed to efficiently deal with situations where the boundaries of the weakly communicating regions are complicated.