ABSTRACT

In this talk, we explore image resolution and the ill-posed-ness of inverse scattering problems.  In particular, we would like to discuss how certain properties of the inclusion might induce high-resolution imaging.  We first explore why resolution matters, and then observe the super-resolution phenomenon with certain particular high contrast inclusion.  We then discuss how local sensitivity (and resolution) around a point is related to the extrinsic curvature of the surface of inclusion around the point.  Along the line, we also discuss concentration of plasmon resonance (in a certain manner) at boundary points of high curvature by quantizing a Hamiltonian flow with the help of the Heisenberg picture, and with the help of an understanding from quantum integrable system.  We then turn to a transmission eigenvalue problem, and observe concentration of almost transmission eigenfunctions along the boundary.  The results discussed in this talk are joint works with Habib Ammari (ETH Zurich), Hongyu Liu (CityU of HK), Keji Liu (Shanghai Key Lab), Mahesh Sunkula (Purdue), Jun Zou (CUHK).

Registration Link:

https://cityu.zoom.us/meeting/register/tJUqduqvpz0jGNFBcqr0SwOLDfYOPMz13f2D