New methods in spectral geometry

本计画旨在利用数学散射理论的方法来解决微分算子的谱分析和指数理论中的问题。这两个领域都是量子现象占主导地位的微米尺度物理材料的理论理解的基础。该项目将在光谱分析和几何学方面发展新的数学成果，并将其成果应用于量子现象的理论模型，其光谱特性处于数学技术范围的极限。解决这些问题预计会影响非交换分析。

This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are at the limit of the range of mathematical techniques. Solving these problems is expected to influence non-commutative analysis.