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Wednesday, May 1, 2019

**Abstract:** A pointwise ergodic theorem for the action of a countable group $\Gamma$ on a probability space equates the global ergodicity (atomicity) of the action to its pointwise combinatorics. Our main result is a short, combinatorial proof of the pointwise ergodic theorem for actions of amenable groups along Tempelman Følner sequences, which is a slightly less general version of Lindenstrauss's celebrated theorem. Without assuming any prior knowledge, we will work up to the general idea of the proof, which stems from Tserunyan's proof of the pointwise ergodic theorem for $\mathbb{Z}$ actions. This is joint work with Jon Boretsky.