Rees and multi-Rees algebras of direct sums of strongly stable ideals

In this talk, we present the known main results and methods to determine Grobner basis for the defining equations of Rees and multi-Rees algebras of direct sums of strongly stable ideals. This allows for classification of families of Rees and multi-Rees algebras that are Koszul, normal and/or Cohen-Macaulay.