Mathematics
Research
A major strength of our mathematics program is the opportunity we give our students to engage in mathematical research early in their degrees. Our much sought-after summer scholarships give second- and third-year students a chance to work with world-class research mathematicians on problems at the breaking edge of mathematical research. This leads naturally into a strong and flexible honours program which has led to many students producing original research of their own in their honours year projects.
The Computer Assisted Research Mathematics and its Applications (CARMA) group has been established to perform research and development relating to the informed use of computers as an adjunct to mathematical discovery. CARMA brings together the expertise from the former Functional Analysis and Discrete Mathematics research groups, with a range of new staff sourced worldwide for their specialist knowledge.
Current research projects include:
- Computational Analysis and Number Theory: computer-assisted study of links between analysis, number theory, knot theory and mathematical physics. Development of mathematical data-mining tools.
- Discrete Mathematics: all aspects of graph theory with emphasis on algebraic graph theory and ties to design theory.
- Linear and Nonlinear Analysis including: convexity; variational methods; fixed point theory; Banach space geometry; frames and wavelet analysis. Applications to dynamical systems, control, optimization, and image or signal reconstruction.
- Optimization and Simulation: models and algorithms for optimization and solution of large-scale problems, using constraint programming and meta-heuristics.
- Topological Groups: structure and auto-morphisms of totally disconnected groups; links to harmonic analysis, geometry, number theory and discrete maths.
- Harmonic Analysis: Fourier analysis, wavelets, time-frequency analysis, sampling and signal processing applications; singular integrals and frames; Clifford analysis and applications to hypercomplex signal processing.
- Number Theory: Arithmetic, algebraic and combinatorial properties of solutions of differential and difference equations; Diophantine analysis.
- Numerical Analysis: Numerical methods for partial differential equations, finite element methods, and approximation theory.
The discipline is also involved in a Cross-Faculty Priority Research Centre with the Faculty of Engineering, Centre for Complex Dynamic Systems and Control.
Publications
The Discipline has an excellent publication record. Information about individual publications is available through the above Research Centres and Group links, and in individual staff profiles.
Seminars
The Discipline holds regular seminars relating to the work of the above research groupings. For information about our seminar program please see the Mathematics Seminars page.
