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Title: Quasi-treeable CBERs are treeable via median graphs

Abstract: A countable Borel equivalence relation (CBER) E on a Polish space X is said to be treeable if there is a Borel forest G ⊂ X² whose trees are precisely the equivalence classes of said relation. E is quasi-treeable if it has a Borel graphing, each of whose components is quasi-isometric to a tree.

In joint work with Ruiyuan (Ronnie) Chen, Antoine Poulin and Anush Tserunyan, we show that quasi-treeable CBERs are treeable by giving a construction of a median graph associated to the quasi-treeing, which will be the main focus of this talk.