CARMA Research Group
Mathematical Analysis and Systems Theory
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
Our experience spans small and fast one-chip implementations to heterogeneous large-scale systems.
Birabahn building of the Wollotuka Institute
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This national and international two-day symposium will address the pressing challenge of how to Indigenise mathematical practice at Universities, both in education and research. The methodology is of collaboration and sharing of knowledge and worldviews from within both Indigenous cultures and the cultures of mathematics and its allied disciplines.