The main goal of the project is a systematic study of embedded eigenvalues of partial differential equations (PDEs) on multi-dimensional unbounded domains. This problem is at the heart of many interdisciplinary problems arising, for instance, in the assessment of optical communication systems, the study of gravity-capillary water waves in fluid mechanics, and the investigation of energy bound states in quantum mechanics. The applicant will also purse in this context her work on drug testing and toxicology. The theory developed over the course of this project, and the applications that will be carried out alongside, are bound to have a major impact in many areas of science.
The applicant is an exceptionally talented researcher who recently made the first significant progress in this area since the 1980's by using scattering theory. A fellowship at the internationally leading nonlinear mathematics group at the University of Surrey will add a new research component in dynamical systems to her already strong back ground. Besides being absolutely essential to the success of the proposed project, this advanced training in dynamical systems, and the additional professional development and community outreach activities at Surrey, will be key to the applicant's development into a mature and independent researcher, thus crucially furthering her future career. An EIF will allow the applicant to return to Europe instead of pursuing her career in the USA, bringing with her valuable knowledge in scattering theory acquired during her stay in Canada and the USA. The project will provide an excellent opportunity to strengthen the European knowledge base in this area.
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