Ilijas Farah - York University When does isomorphism of uniform Roe algebras associated imply coarse equivalence of the underlying coarse spaces? A recent result of Spakula and Willett gives sufficient conditions in the case of coarse metric spaces. These conditions are uniform discreteness and property A (the "coarse" analogue of amenability). I’ll discuss recent progress on weakening these conditions. No previous knowledge of coarse spaces, Roe algebras, or logic is required. (This is a joint work with Bruno De Mendoca Braga.)