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.