Mathematical Physics and Harmonic Analysis Seminar
Date: May 8, 2020
Time: 1:50PM - 2:50PM
Location: Zoom seminar
Speaker: Wei Li, LSU
Title: Zoom Seminar: Embedded eigenvalues of the Neumann Poincaré operator
Abstract: The Neumann-Poincaré (NP) operator arises in boundary value problems, and plays an important role in material design, signal amplification, particle detection, etc. The spectrum of the NP operator on domains with corners was studied by Carleman before tools for rigorous discussion were created, and received a lot of attention in the past ten years. In this talk, I will present our discovery and verification of eigenvalues embedded in the continuous spectrum of this operator. The main ideas are decoupling of spaces by symmetry and construction of approximate eigenvalues. This is based on two works with Stephen Shipman and Karl-Mikael Perfekt.