Geometric Spectral and Scattering Theory

光谱和散射理论是对几何、物理和工程中出现的系统的固有频率（特征值）和振动模式（特征函数）的数学研究。因此，它在许多领域都有重要的应用，包括医学成像、地质调查和沿光纤传输信息。在这个项目中，我将解决各种问题，包括特征值的高频渐近性，量子混沌，特征函数集中和非线性波传播。

Spectral and scattering theory is the mathematical study of natural frequencies (eigenvalues) and modes of vibration (eigenfunctions) of systems arising in geometry, physics, and engineering. As such, it has important applications in numerous areas including medical imaging, geological surveying and the transmission of information along optical fibres. In this project I will solve a variety of problems involving high-frequency asymptotics of eigenvalues, quantum chaos, eigenfunction concentration and nonlinear wave propagation.