Dragomir Saric of the Institute for Advanced Study presents a seminar on the ergodicity of geodesic flows on infinite Riemann surfaces, delivered at the joint IAS/PU Groups and Dynamics Seminar. He shows that the hyperbolic geodesic flow of such a surface is ergodic exactly when Brownian motion on it is recurrent, a condition also equivalent to divergence of the Poincare series. Saric gives sufficient conditions on Fenchel-Nielsen parameters for a surface to fall into this class, and proves a version of a conjecture by J. Kahn and V. Markovic stating that a surface with arbitrarily large cuff lengths and one topological end has an ergodic geodesic flow once the twist parameters are chosen appropriately. The results draw on joint work with Ara Basmajian, Hrant Hakobyan, and Michael Pandazis. The talk runs 71 minutes and is pitched at researchers in Teichmuller theory and hyperbolic geometry.