250218 András Vasy

In this lecture I will describe a microlocal (or phase space based) framework for the Fredholm (invertibility up to finite rank obstacles) analysis of non-elliptic problems both on manifolds without boundary and manifolds with boundary (or corners). Examples in which such a framework (or a similar framework) has recently been useful include wave propagation on black hole spacetimes, which is a key analytic ingredient for showing the stability of black holes, analysis of the resolvent of the generator of the flow for dynamical systems, which is the key tool for the analysis of the Ruelle zeta function, and Feynman propagators in quantum field theory, which are useful for analysis of the spectral zeta function on Lorentzian spacetimes. The speaker’s contributions to this are partly joint work with collaborators: Nguyen Viet Dang, Jesse Gell-Redman, Nick Haber, Dietrich Häfner, Peter Hintz and Michał Wrochna.