The coarse-geometric rigidity conjecture for uniform Roe algebras

Let $(X,d)$ and $(Y,\partial)$ be uniformly locally finite metric spaces. Their uniform Roe algebras $C^*_u(X)$ and $C^*_u(Y)$ are the norm closures in $\mathcal{B}(\ell^2(X))$ and $\mathcal{B}(\ell^2(Y))$, respectively, of the $*$-algebras of bounded operators with controlled propagation. The spaces are coarsely equivalent when they are isomorphic in the coarse category, and bijectively coarsely equivalent when there is a bijective coarse equivalence between them.

Uniform Roe algebra rigidity conjecture. The $C^*$-algebras $C^*_u(X)$ and $C^*_u(Y)$ are Morita equivalent (respectively, isomorphic) if and only if $(X,d)$ and $(Y,\partial)$ are coarsely equivalent (respectively, bijectively coarsely equivalent).

This conjecture asks whether uniform Roe algebras completely determine the coarse geometry of uniformly locally finite metric spaces, with Morita equivalence corresponding to coarse equivalence and isomorphism corresponding to bijective coarse equivalence. The supplied text does not state whether it has been resolved.