Description
I will discuss a microlocal analysis approach to local spectral zeta function densities on classes of pseudo-Riemannian manifolds including asymptotically Minkowski spaces. The poles are shown to be local geometric invariants, whereas renormalized trace densities provide a rigorous definition of physical quantities in Quantum Field Theory. A key role is played by the asymptotic dynamics arising from suitable spacetime compactifications. This is joint work with Nguyen Viet Dang and Andras Vasy, with ongoing work on extensions also by/with Ashkan Sadat Kyaee and Mikhail Molodyk.