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Speaker: Peter Burton (Iowa State University)

Abstract: We will introduce the concept of soficity for a countable discrete group, which generalizes both residual finiteness and amenability. Notably, it is a major open problem to determine whether every countable group is sofic, although the answer is widely believed to be negative. The primary relevance of the assumption that a group is sofic is to ensure that various computations related to its symbolic dynamics and ergodic theory have the expected results, and we will sketch how these arguments proceed.