New methods in spectral geometry

这个项目的目的是利用数学散射理论中的方法来解决微分算子的谱分析和指数理论中的问题。这两个领域都支持在微观长度尺度上对物理材料的理论理解，其中量子现象占主导地位。该项目将在光谱分析和几何方面开发新的数学结果，并将其结果应用于光谱特性处于数学技术范围极限的量子现象的理论模型。这些问题的解决有望影响非对易分析。

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.