This course presents a comprehensive exploration of mathematical theories on metamaterials within wave systems including acoustics, electromagnetics, and elasticity. The analytical methodologies encompass both the potential theory and the variational approach. Subsequently, the course delves into the practical applications including cloaking invisibility and imaging. Regarding invisibility, we mainly focus on the exceptional phenomenon known as cloaking due to anomalous localized resonance. At last, the mathematical theory on the fabrication of the metamaterial shall be introduced.
partial differential equation, potential theory, Sobolev space
1. D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer Cham, 2019.
2. H. Ammari and H. Kang Polarization and Moment Tensors: with Applications to Inverse Problems and Effective Medium Theory. Springer-Verlag, New York, 2007.
Target Audience: Undergraduate students, Graduate students
Teaching Language: Chinese
Dr. Hongjie Li holds the position of Assistant Professor at the Yau Mathematical Sciences Center. He obtained his Ph.D. in Applied Mathematics from the Hong Kong Baptist University in 2019. Dr. Li's research encompasses a range of areas including inverse problems, partial differential equations, mathematical materials science, asymptotic and spectral analysis, finite element methods, numerical analysis and scientific computing. He has published several papers in esteemed Applied Mathematics journals, such as the Journal de Mathématiques Pures et Appliquées, SIAM Journal on Mathematical Analysis, SIAM Journal on Applied Mathematics and ESAIM: Mathematical Modelling and Numerical Analysis. During his doctoral studies, Dr. Li was granted the prestigious Hong Kong Ph.D. Fellowships for three years by the Research Grants Council of the Hong Kong Government, along with the Yakun Scholarship Scheme. Subsequently, his remarkable academic journey was acknowledged with the Hong Kong Mathematical Society Best Thesis Award in 2021.