Geometric topological facts about spaces are generally established by computations carried out on associated algebraic invariants. A subtle new invariant known as elliptic homology is descended from an ancient idea of Euler (1756) via a modern insight of Quillen (1969) and work of the principal investigator and a few others. He and his collaborator, Peter S. Landweber of Rutgers University, will continue to study elliptic homology, trying at the same time to tame its computational obstacles and to display more plainly its relation to its geometric roots. The hope is that new geometric information will become accessible as a culmination of these efforts.
