报告题目：Mathematics and Computation of Inverse Scattering Problems
报告摘要：Inverse scattering problems arise in diverse areas of industrial and military applications, such as nondestructive testing, seismic imaging, submarine detections, optical imaging, and medical imaging. A model scattering problem is concerned with a given wave incident on a medium enclosed by a bounded domain. The problemis to determine the scattered field or the energy distribution for the known scatterer. The inverse problem is to determine the scatterer from the boundary measurements of the fields. Although this is a classical problem in mathematical physics, mathematical issues and numerical solution of the inverse problemremain to be challenging since the problem is ill-posed and computational complexity! The significant challenges have thus far limited in many ways the scope of inverse problem methods in practical applications. They also present great opportunities for a source of many exciting new problems in mathematical and computation. In this talk, the speaker will first introduce inverse scattering problems of acoustic and electromagnetic wave propagation. Recent stability results and techniques for the inverse problems will be presented. A stable continuation approach based on multi-frequency data will also be presented. The speaker will also highlight related topics on nano-optics and scattering and inverse scattering in elasticity.