Resonance free strips for normally hyperbolic trapped sets

The talk will provide a review of joint work with Nonnenmacher on resonance free strips for filamentary hyperbolic trapped sets, and with Wunsch on normally hyperbolic trapped sets. Recent advances due to Vasy
and Datchev-Vasy allow more general infinities than in the orignal papers.
I will also describe current work with Nonnenmacher on precise estimates of the resonance free gap in the normally hyperbolic case.