Ken Ono's research interest is in number theory. He has worked actively on questions related to Diophantine equations, partitions, L-functions, elliptic curves and modular forms. These objects are the main players in Wiles' proof of Fermat's Last Theorem, and they are the subject of intense investigation. 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. Arun Ram's research centers around the connections between combinatorics, symmetry groups, geometry, and harmonic analysis. The main goal is to understand how symmetry groups can act on vector spaces and whether these actions can be understood combinatorially.