Multiresolution homogenization has been developed over the last decade as a computational and analytical technique for homogenization of PDE's
and differential operators. One of the chief remaining difficulties lies in practical extension of the technique to higher dimensional
problems. Separated representations, aka Kronecker products, have been garnering attention as a promising approach to the problem of
representing operators and functions in high dimensions. In this talk we present some recent numerical and analytical results of applying
multiresolution homogenization to operators in separated form. Applications such as homogenization of elliptic operators, wave
propagation, eigenvalue problems, etc. will be discussed as time permits.