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# Jeffrey Galkowski, Northeastern University – Wunsch/PDE Mini-school

## December 6, 2018 @ 4:00 pm - 5:00 pm

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**Title:** Optimal Resolvent Estimates in Non-trapping Geometries

**Abstract:** In this talk we discuss how propagation estimates can be used to prove resolvent estimates in non-trapping geometries. We will introduce the notion of defect measures and prove propagation estimates in this setting. We will then use these estimates to prove a non-trapping resolvent estimate and finally refine the estimates to give optimal bounds on the resolvent. Time permitting we discuss the necessary modification when the manifold has a boundary.