This research, supported by the National Science Foundation Young Investigator award, will study indices of elliptic operators on non-compact manifolds. The information is encoded in various homologies which are invariants of the large scale structure of the manifold. Singular spaces will be studied by viewing them as a collection of non-compact manifolds glued according to their large scale structure. The National Science Foundation Young Investigator awardrecognizes outstanding young faculty. This award recognizes the recipient's strong potential for continued professional growth as a research mathematician and for significant development as a teacher and academic leader.
