In 2004, I conjectured that the quasi-isometry problem for finitely generated groups was strictly harder than the isomorphism problem; but unfortunately I was only able to prove that the quasi-isometry problem was not smooth. In this talk, making essential use of techniques developed by Harvey Friedman and Robin Tucker-Drob, I will show that the quasi-isometry problem does not Borel reduce to an essentially free countable Borel equivalence relation.
TBA