The diffraction of waves is a phenomenon whose study dates back to at least the 17th century, but remains a challenge for
rigorous analysis. I will discuss some recent work on the phenomenon of diffraction by conic singularities, and its application to the analysis of the spectrum of the Laplace operator and the distribution of resonances in scattering theory. We expect that an acoustic wave striking the exterior of a polygon should cause prolonged ringing (`resonance') which would not be present for a smooth obstacle, and I will present some results to substantiate this claim. Speaker(s): Jared Wunsch (Northwestern University)