Objective "This project will focus on the development of new methods for the study of spectral problems of non-selfadjoint operators and the application of these methods to real-world problems. We will organise a range of activities to promote our research and, more generally, mathematical analysis to scientists and students.Non-selfadjoint operators and spectral problems arise naturally in many application areas such as hydrodynamics and MHD, lasers, scattering and inverse scattering problems, and numerical methods for photonic crystal fibres. The spectral behaviour of these operators exhbits many new phenomena compared to selfadjoint operators. The spectral theorem and variational principles are not valid. Unable to make use of these methods, we turn to an exciting technique, boundary triples, with which we have already recently obtained very general results for PDEs under minimal and natural hypotheses, with few technical complications.Our first problem we will consider is the explicit construction of a functional model for a wide class of operators. This will yield many new results for differential operators in terms of their coefficientsrather than in completely abstract terms as at present. Our second problem is to analyse the `detectable subspace' in inverse problems: the maximal part of the operator which can be reconstructed from boundary measurements. Further problems will include PT-symmetric operators and operators with almost Hermitian spectrum. Finally, we will investigate in detail a class of highly singular ODEs.Our outreach activities will include the organisation of two workshops for scientists, several lecture series, as well as a summer school for postgraduates and some workshops for undergraduate students." Fields of science natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysisnatural sciencesphysical sciencesopticslaser physics Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) FP7-PEOPLE-2011-IIF - Marie Curie Action: "International Incoming Fellowships" Call for proposal FP7-PEOPLE-2011-IIF See other projects for this call Funding Scheme MC-IIF - International Incoming Fellowships (IIF) Coordinator UNIVERSITY OF KENT EU contribution € 278 807,40 Address THE REGISTRY CANTERBURY CT2 7NZ Canterbury, Kent United Kingdom See on map Region South East (England) Kent East Kent Activity type Higher or Secondary Education Establishments Administrative Contact Kate Ludlow (Mrs.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
