A semiclassical approach to spectral theory

谱理论是研究几何学、量子物理学和工程学中出现的系统的固有频率(特征值)和振动模式(特征函数)的数学分支。因此，它们在地震和医学成像、纳米技术和光通信中有重要的应用。这个项目旨在使用最近发展的数学工具来促进我们对高能本征值和本征函数的理解，以及用于数值计算它们的新算法。

Spectral theory is the branch of mathematics dealing with natural frequencies (eigenvalues) and modes of vibration (eigenfunctions) of systems arising in geometry, quantum physics and engineering. As such, they have important applications in seismic and medical imaging, nanotechnology, and optical communications. This project aims to use recently developed mathematical tools to advance our understanding of high energy eigenvalues and eigenfunctions, as well as new algorithms for numerically computing them.