Jeffrey Galkowski (Stanford)

The Analysis and PDE Seminar will take place on Monday, December 7th 2015, from 4:10-5:00 pm in Evans Hall, room 740.

Speaker: Jeffrey Galkowski (Stanford)

Title: Resonance Free Regions and Average Smoothing Times

Abstract: We give a quantitative version of Vainberg’s method relating pole free regions to propagation of singularities. In particular, we show that there is a logarithmic resonance free region near the real axis of size \tau with polynomial bounds on the resolvent if and only if the wave propagator gains derivatives at rate \tau. Next we show that if there exist singularities in the wave trace at times tending to infinity which smooth at rate \tau, then there are resonances in logarithmic strips whose width is given by \tau. As our main application of these results, we give generically optimal bounds on the size of resonance free regions in scattering on geometrically nontrapping manifolds with conic points and exteriors of nontrapping polygonal domains.

See you all there!