# Resonances for Normally Hyperbolic Trapped Sets

 Analysis Seminar Topic: Resonances for Normally Hyperbolic Trapped Sets Speaker: Semyon Dyatlov Affiliation: University of California Date: Tuesday, April 2 Time/Room: 3:15pm - 4:15pm/S-101

Resonances are complex analogs of eigenvalues for Laplacians on noncompact manifolds, arising in long time resonance expansions of linear waves. We prove a Weyl type asymptotic formula for the number of resonances in a strip, provided that the set of trapped geodesics is r-normally hyperbolic for large r and satisfies a pinching condition. Our dynamical assumptions are stable under small smooth perturbations and motivated by applications to black holes. We also establish a high frequency analog of resonance expansions.