Title: Selected Topics in Mathematical Studies of Optics and Photonics

Abstract: This talk is concerned with the analysis and computation for light-structure interactions in nano devices. I will start with an overview of my research program, and then focus on two types of mathematical problems arising from the control of electromagnetic waves in engineered nanostructures: extraordinary field enhancement in metallic nanogaps and super-resolution imaging of nanostructures. The fundamental mathematical issues will be examined from both analytical and numerical perspectives. The ongoing and future works will also be discussed briefly.