Embedded eigenvalues of the Neumann Poincaré operator

Math Physics Seminar
Thursday, April 23, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Wei Li – Louisiana State University – liwei@lsu.edu
Rui Han

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.