CARMA Research Group

Mathematical Analysis and Systems Theory

About us

Leader: Jeff Hogan

The group has wide-ranging expertise in many branches of mathematical analysis, including harmonic, functional, nonlinear, nonsmooth and geometric analysis. In particular, our members work in:

* Fourier analysis -- wavelets and other tools for signal and image processing;

* Clifford analysis -- higher-dimensional function theory with applications to multichannel mutivariable signal processing

* Geometry in Banach spaces and convex metric spaces

* Numerical methods for partial differential equations, including finite element methods

* Approximation theory

* Variational methods, with applications to image processing

* Control theory, with applications to energy systems, climate economics and cyber-security

* Geometric analysis -- calculus of variations

* Optimisation (theoretical and numerical) with applications to signal and image processing, including compresssed sensing

* Experimental mathematics, with emphasis on optimisation

Systems theory is, in a broad sense, the theory of mathematical processes that evolve with time. These processes, also called dynamical systems, are often described by differential or difference equations. In these cases the systems are referred to as continuous and, respectively, discrete-time dynamical systems. If a system can be influenced from the outside, it is called a control system. The expertise and interests of our research group cover stability theory of differential and difference inclusions, which are generalisations of the aforementioned concepts. This goes along with applications in areas such as

* climate economics

* communications

* control

* optimisation

Our experience spans small and fast one-chip implementations to heterogeneous large-scale systems.