The group in applied mathematics works with the development of mathematical methods in spectral and scattering theory, partial and ordinary differential equations, semiclassical analysis and microlocal analysis in relation to different phenomena in quantum mechanics, wave propagation and biology. In addition, the group works with signal and image analysis.
The following fields are part of the research within Applied Mathematics:
Spectral and scattering theory
The group studies the spectral properties of one-body Schrödinger and Dirac type operators using both the generalization of exact Gelfand- Levitan-Marchenko inverse spectral theory and asymptotical semiclassical methods, and inverse problems in wave propagation. The group also deals with applications of the semiclassical description of surface and body waves and inverse spectral and resonance problems to recover the inner Earth and planets structure from the surface or close-to-surface seismic measurements.
Mathematical biology and epidemiology
The group applies the ordinary differential equation (ODE) approach to study the dynamics of infectious diseases and the associated control mechanism, the interaction of different species and stabilization/destabilization phenomena in ecosystems.
Image analysis and remote sensing
The group develops the partial differential equation (PDE) methods in image analysis which are numerically stable and have the ability to extract important features (e.g., edges, cups) of the image. The group applies signal- and image analysis methods to data from earth-observing satellites to extract information on e.g., variations in vegetation and ecosystems on a local to the global scale as a result of climate change.