Rigidity for uniform Roe algebras

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.)

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