Passman's Research Donald S. Passman works in group theory, ring theory and the interplay between the two subjects. Specifically, he is interested in group algebras, which are rings constructed from groups.
Group algebras have important applications to both finite and infinite group theory.
Furthermore, certain generalizations called skew group rings and crossed products have important ring-theoretic consequences. In the case of group algebras of infinite groups, one knows, for example, when they have nilpotent ideals, when they are prime rings, when they are Artinian, and when they satisfy a polynomial identity. Thus, we understand a good deal about group algebras, but there is much more to learn.