Borel asymptotic dimension

This talk will focus on discussing the recent paper "Borel asymptotic dimension and hyperfinite equivalence relations" by Clinton, Jackson, Marks, Seward, and Tucker-Drob. They introduce the definition of asymptotic dimension from the setting of coarse geometry to the setting of Borel equivalence relations and use it to provide some alternate proofs and generalized proofs of past hyperfiniteness results. In particular, they get examples of exponential growth groups whose every free Borel action is hyperfiniteness.