Inverse problems arise in diverse areas of industrial and military applications, such as nondestructive testing, seismic imaging, submarine detections, near-field and nano optical imaging, and medical imaging. A model problem in wave propagation is concerned with a plane wave incident on a medium enclosed by a bounded domain. Given the incident field, the direct problem is to determine the scattered field for the known scatterer. The inverse problem is to determine the scatterer from the boundary measurements of near field currents densities. Although this is a classical problem in mathematical physics, mathematical issues and numerical solution of the inverse problems remain to be challenging since the problems are nonlinear, large-scale, and most of all ill-posed! The severe ill-posedness has thus far limited in many ways the scope of inverse problem methods in practical applications. In this talk, the speaker will first introduce general inverse problems and discuss the state of the arts of the inverse problems. Our recent progress in mathematical analysis and computational studies of the inverse boundary value problems will be reported. Several classes of inverse problems will be studied, including inverse medium problems, inverse source problems, inverse obstacle problems, and inverse waveguide problems. A novel stable continuation approach based on the uncertainty principle will be presented. By using multi-frequency or multi-spatial frequency boundary data, our approach is shown to overcome the ill-posedness for the inverse problems. New stability results and techniques for the inverse problems will be presented. Related topics will be highlighted.

包刚，现任浙江大学数学科学学院教授、院长。1985年毕业于吉林大学，1991年在美国莱斯大学获应用数学博士学位，1991-1994年先后在美国莱斯大学、明尼苏达大学数学及其应用研究所做博士后研究，1994-1999年在佛罗里达大学任助理教授、副教授，1999年应聘为密歇根州立大学教授，并创建美国密歇根州立大学密西根工业与应用数学中心。包刚教授2001年入选教育部长江学者特聘教授(吉林大学)， 2003年获冯康奖，2005年获国家杰出青年基金（B类）。主要致力于偏微分方程中的反问题，衍射光学、非线性光学、近场及纳米光学等波传播问题的系统研究，是上述领域数学理论和科学计算的国际领军人物。多次应邀在重要国际会议作大会报告，论文发表在包括国际顶尖刊物J. Ameri. Math. Soc.， Arch. Ration. Mech. Anal., J. Math Pures Appl., Trans. AMS, Math. Comp.,  Comm. PDE, SIAM系列含SIAM News等学术期刊达150余篇。包刚教授现任国务院学位委员会学科评议组成员，中国数学会，中国工业与应用数学，中国计算数学会常务理事。担任SIAM J. Appl. Math., Inverse Problems, Journal of Differential Equations, J. Inverse Problems and Imaging等10余个国际著名学术刊物编委。