DMS Colloquium: Dr. Junshan Lin

Speaker: Dr. Junshan Lin (Auburn)

Title: Electromagnetic Wave in Novel Materials and Devices: Mathematical Analysis and Numerical Computation

Abstract: The advance in fabrication technology allows for the manipulation of electromagnetic waves at various scales by novel materials and devices. The applications of these materials and devices in physics and engineering have driven the need for mathematical studies to guide their experimental designs. In particular, rigorous mathematical theories need to be established to understand new types of wave-matter interactions; efficient computational methods need to be developed for the modeling of wave phenomena in complex media and solving related inverse problems for their applications.

In this talk, I will first give an overview of my research along this direction. Then I will exemplify how mathematical research contributes to these aspects by using one specific project on resonant wave scattering in subwavelength structures (structures with features much smaller than the operating wavelength). I will present quantitative mathematical theories for various resonance phenomena arising in different subwavelength structures and fast numerical methods for their computational modeling. I will also introduce the mathematical framework for the application of resonances in biosensing and imaging.