# Resonances for Normally Hyperbolic Trapped Sets

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Semyon Dyatlov, UC Berkely
Fine Hall 314

(PLEASE NOTE SPECIAL TIME.)  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 and revisit exponential decay of highly oscillating waves on Kerr-de Sitter and Kerr black holes.