Mathematical Sciences: Research in Scattering Theory

本课题将用波动方程方法简化负曲率对称空间的调和分析，并推广双曲流形上波动方程的微扰理论。新理论的目的是将其应用于商空间和带扭转的双曲流形。这个项目解决了基本的数学问题，在物理和化学方面有潜在的应用。

This project will simplify a wave equation approach to harmonic analysis for symmetric spaces of negative curvature and extend a perturbation theory for the wave equation on hyperbolic manifolds. The new theory is aimed at applications to quotient spaces and hyperbolic manifolds with twist. This projects addresses fundamental mathematical questions with potential applications for physics and chemistry.