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BIRS Workshop Lecture Videos

Diffraction of semiclassical singularities by conormal potentials Wunsch, Jared


Consider a semiclassical Schr\"odinger operator $P=h^2\Delta+V-E,$ where $V$ has a conormal singularity along a hypersurface.  The singular structure of $V$ affects the propagation of semiclassical singularities for solutions to $Pu=0,$ and in particular there is a `diffraction' of wavefront set by the interface: singularities are reflected as well as transmitted as they cross the interface transversely.  The reflected wave, however, is more regular, with the improvement depending on the regularity of the interface; moreover singularities cannot (for high enough regularity) glide along the interface.  (Joint work with Oran Gannot.)

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