Since the discovery of quantum theory we know that spectral theory of linear operators in Hilbert spaces is fundamental in our description of nature. Apart from its significance in the formulation of quantum mechanics, spectral theory has also been very influential in other areas of pure and applied mathematics. The proposed programme is broadly about novel applications of spectral methods in general relativity such as "Spectral Theory of Stationary Spacetimes", "Stability questions in General Relativity", and "The Mathematics of QFT and Hawking Radiation".
