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Explore the fascinating world of perfect matchings in hyperfinite graphings in this one-hour lecture by Gabor Kun. Delve into the geometric structure of amenable groups and hyperfinite graphings, focusing on their bipartite cases and the typical existence of perfect matchings. Discover how recent breakthroughs in this field have led to significant advancements, including the solution to Tarski's circle squaring problem using measurable and Borel pieces. Examine the wide-ranging applications of perfect matchings, from probability theory to group theory and measurable equidecompositions. This talk, part of the Measured Group Theory series at the Centre de recherches mathématiques, offers valuable insights into this tractable yet powerful mathematical concept.
