Colloquium Mathematics - Matteo Capoferri, University College London

Title: Wave propagator on Riemannian manifolds

Abstract:

In my talk I will present a global, invariant and explicit construction of hyperbolic propagators on closed Riemannian manifolds, focussing in particular on the wave propagator. Here the propagator is the operator that maps initial conditions to a solution of the wave equation and “explicit” means reducing the problem to integration of ordinary differential equations. This can be achieved by representing the propagator as a single Fourier integral operator with distinguished complex-valued phase function, global both in space and in time. The knowledge of the propagator allows one, in turn, to recover asymptotic spectral properties of the operators at hand.