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Explore advanced concepts in measured group theory through this 45-minute lecture on Poisson boundaries without moment conditions. Delve into a new method called the "pin down approximation criterion" for identifying Poisson boundaries of hyperbolic groups with finite entropy measures. Learn how this approach overcomes limitations of previous techniques, providing the first examples of Non-Choquet Deny groups where the Poisson boundary can be identified for all finite entropy measures. Focus on the key example of the free group and gain insights into this groundbreaking research, which is a collaborative effort with Kunal Chawla, Behrang Forghani, and Giulio Tiozzo. No prior knowledge of hyperbolic groups is required to benefit from this mathematical exploration presented at the Centre de recherches mathématiques (CRM) as part of the Measured Group Theory program.
