Operators, Asymptotics, Waves

Kirill's research interests are in the multi-scale asymptotic analysis of materials and media. The main objective of such analysis is to replace the complex medium in question by its "effective" counterpart possessing the physical properties of the original problem that are deemed important in a given application. Kirill uses a range of tools from the asymptotic analysis of partial differential equations and integral functionals, which are often linked to the kind of convergence ("topology") that preserves the energy stored in a medium for any data from a given function class. An example of a recent evolution of such asymptotic tools is provided by the analysis of the overall ("averaged", "homogenised") behaviour periodic composite media, where the increased contrast between component media leads to a loss of compactness of solutions (more generally, of bounded-energy sequences) in the classical Sobolev spaces.

 
Karl-Mikael is an Associate Professor in mathematical analysis at the Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), Norway, and Visiting Member of the Academic Staff at the Department of Mathematics and Statistics, University of Reading, UK.
 
His research interests roughly lie within the areas of operator theory, potential theory, complex analysis, and spectral theory.

Euan is Professor of Mathematics at the University of Bath. His research lies at the interface between semiclassical analysis and numerical analysis of partial differential equations (PDEs), and is interested in problems involving the scattering of acoustic and electromagnetic waves.