Neumann-Poincaré (NP) operators are classical boundary integral operators in potential theory. Recently, the study of the spectral properties of NP operators has called great attention due to its intriguing connections to a variety of cutting-edge topics including plasmonics and metamaterials, invisibility and super-resolution imaging in wave scattering theory. In this talk, I shall discuss our discoveries in this field, especially on the spectral patterns of the NP eigenfunctions induced by the local and global geometries of the underlying boundary surface, as well as several interesting applications.
About the Speaker:
Hongyu Liu is a professor of mathematics at City University of Hong Kong. He obtained his PhD in mathematics from The Chinese University of Hong Kong in 2007, and held faculty positions at Hong Kong Baptist University, University of North Carolina at Charlotte (USA), University of Reading (UK), and University of Washington at Seattle (USA). His research interest includes inverse problems and imaging, wave propagation, analysis and PDEs, mathematical materials science, scattering theory and spectral theory, mean field games and scientific computing. His research recognition includes the Calderón Prize by Inverse Problems International Association (IPIA), the Hong Kong Mathematical Society Young Scholar Award, Changjiang Chair Professorship by Ministry of Education of China, and Fellow of IOP, Institute of Physics, UK. He is a founding Editor-in-Chief of the journal, Communications on Analysis and Computation.