Perfect Matchings in Hyperfinite Graphings - Lecture 2

Explore the intricacies of perfect matchings in hyperfinite graphings in this 44-minute lecture by Gabor Kun, part of the Measured Group Theory series at the Centre de recherches mathématiques. Delve into the geometric structure of amenable groups and hyperfinite graphings, focusing on the existence of perfect matchings in bipartite cases. Discover recent breakthrough results related to perfect matchings, including the solution to Tarski's circle squaring problem using measurable and Borel pieces. Examine applications ranging from probability theory to group theory and measurable equidecompositions, highlighting the versatility and importance of perfect matchings in various mathematical domains.