The principal investigator will study an important invariant associated to elliptic operators on manifolds with boundary. His method will involve calculation of this invariant, the so called eta invariant, of the boundary value problem. The research involved here involves a wide variety of areas of mathematics. The primary objects of study are partial differential operators and manifolds. What is important is the relationship of certain quantities associated with both the operator and the geometry of the manifold (a manifold is a higher dimensional analog of a surface). The principal investigator will concentrate on one such quantity, the eta invariant.
