Geometric Spectral and Scattering Theory

光谱和散射理论是对几何学、物理学和工程学中出现的系统的固有频率（本征值）和振动模式（本征函数）的数学研究。因此，它在许多领域具有重要的应用，包括医学成像、地质勘测和沿沿着光纤的信息传输。在这个项目中，我将解决各种各样的问题，包括本征值的高频渐近性，量子混沌，本征函数浓度和非线性波传播。

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.