Significant research is being carried out in the Department in these areas of Mathematics:
- Algebraic combinatorics
- Graph theory and combinatorics
- Mathematical and computational relativity
- Mathematics of evolutionary biology
- Numerical analysis and uncertainty quantification
- Point patterns and processes
- Quantitative Genetics
- Semiclassical and harmonic analysis
- Stochastic integro-differential equations and their applications
Research group: Mathematics of evolutionary biology
Evolutionary biology has proven to be a rich source of mathematical, statistical and computational challenges. This is particularly true in the genomics age with the explosion in the quantity and diversity of biological data available. It is now commonplace to sequence entire genomes of organisms to investigate evolutionary questions. Indeed, researchers are sequencing entire populations or communities of organisms. To analyse these data we draw on many varied fields of mathematics, and invent new ones.
Mike Hendy and David Bryant have worked extensively on many areas of evolutionary biology and genetics. They are especially well-known for their contributions to phylogenetics, which is the reconstruction of evolutionary history from genomic data. The methods they have developed are in wide use across a range of application areas. Mike was a founding director of the Allan Wilson Centre, a centre of research excellence, and David is currently a Principal Investigator.
Jessica Leigh (postdoc supported by the Allan Wilson Centre) has a background in genetics and computing, and is designing new tools for visualising sequence data in populations. Josh Collins is completing a Marsden-funded Ph.D. on the detection of hybridisation between species. Gordon Hiscott is an Allan Wilson Centre funded Ph.D. student working on techniques for population analysis of whole genome data. Monika Balvočiūtė is a Ph.D. student funded by an Otago scholarship working on mathematical and combinatorial problems arising in the visualisation of complex evolutionary signals.