Survey of the inverse spectral problem for the Notices of the ICCM
arXiv:1504.02000
Abstract
This is an updated survey on the inverse spectral problem written for the Notices of the ICCM. It rapidly reviews some of the material in the previous survey of the same title (arXiv:math/0402356) and then discusses some relatively new results (rigidity results for the ellipse, phase shifts in scattering theory). The last section poses a number of open problems involving "inverse results for oscillatory integrals".