Mathematical Sciences: Heat Equation Asymptotics with Pseudo Differential Boundary Conditions

该奖项将支持具有广义边界条件的热方程渐近性研究。边界条件将是Atiyah、Patodi和Singer类型。本研究将包括研究结构在边界附近不是乘积的厄米矩阵的Dolbeault复形和具有边界的流形的eta不变量。该奖项支持的研究涉及全局分析和光谱几何的各个方面。全局分析试图将空间的拓扑性质与解析性质联系起来。谱几何研究空间的几何与空间上定义的微分算子的不变量之间的关系。

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.