Mathematical Sciences: Heat Equation Asymptotics with Pseudo Differential Boundary Conditions

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This award will support research on heat equation asymptotics with generalized boundary conditions. The boundary conditions will be of Atiyah, Patodi, and Singer type. The research will include a study of the Dolbeault complex for a Hermitian matrix where the structures are not product near the boundary and the eta invariant of a manifold with boundary. The research supported by this award involves aspects of global analysis and spectral geometry. Global analysis attempts to relate topological properties of a space with analytic properties. Spectral geometry studies the relationship between the geometry of a space and invariants of a differential operator defined on the space.