The strategic vision for the University of Otago is to be a research-led University with an international reputation for excellence. The Department of Mathematics and Statistics carries out significant research in the fields of mathematics, statistics and data science.

## Mathematics

### Algebra and Discrete Mathematics, Computation and Applications

Algebra is the study of abstract mathematical structures. Discrete Mathematics is a grab-bag term for any branch of mathematics which doesn’t focus on continuous spaces and objects.

Our research ranges from algebraic combinatorics and combinatorial representation theory to discrete geometry and computational biology. This work has concrete applications in statistics, operations research, genetics and evolutionary biology.

Our researchers:

### Partial Differential Equations and Applied Analysis

Analysis is, broadly speaking, the branch of mathematics that deals with limits and change. This includes the familiar operations of differentiation and integration from calculus, as well as differential equations, the study of functions of real or complex variables, and numerical analysis (among many others!).

Our research group has particular strengths in differential equations (including well-posedness, asymptotic behavior, and singular limits of solutions), harmonic analysis (the study of functions and operators via oscillations), stochastic processes (including continuous time random walks), and applied analysis (including fractionalcalculus, anomalous dispersion, pattern formation, and nonlinear waves).

Our researchers:

### Fluids and Waves

Fluid mechanics and wave propagation phenomena are branches of physics and applied mathematics. Fluid mechanics models the flow of fluids (i.e., liquids, gases and plasmas), while wave propagation describes the motion of disturbances (e.g., water waves, sound waves, electromagnetic waves and elastic waves) that transport energy through a medium but not matter.

Our research group uses analytical and numerical techniques, e.g., asymptotic analysis, spectral methods and computational fluid dynamics, to solve a range of fundamental and applied problems in fluid mechanics, acoustics, scattering theory, physical oceanography, environmental fluid mechanics, renewable energy and metamaterials science.

Our researchers:

### Mathematical Physics

Mathematical physics involves the development and application of mathematical tools to the solution of problems arising in modern physics. General relativity and quantum mechanics are the two leading fundamental theories in modern physics. General relativity is concerned with the interaction between matter, energy, space and time, and it explains gravity as a geometric property of a curved four-dimensional spacetime continuum. Quantum mechanics is a probabilistic theory of physical reality at the scale of the atoms and fundamental particles.

In the mathematical physics group, we have active research programs in relativity, astrophysics, quantum theory, and partial differential equations. In particular, the mathematical and computational relativity group is long-established and focusses on gravitational waves, the global structure of spacetimes, black holes, as well as cosmological models and the early universe.

See our Mathematical and Computational Gravity group website

Our researchers:

## Statistics

### Ecological and Environmental Statistics

- Bayesian modelling
- Capture-recapture
- Population modelling
- Conservation biology
- Experimental design
- Climate change

### Spatial and Spatio-temporal Modelling

- Spatial statistics
- Earthquake and volcanic hazard modelling
- Point process models
- Network models
- Geostatistics
- Spatial epidemiology
- Cosmology and astrostatistics

### Statistics in the Health and Life Sciences

- Bioinformatics
- Clinical trials
- Statistical epidemiology
- Evolutionary biology
- Statistical genetics
- Physiology
- Survival models
- Genomics

### Statistical Theory and Methodology

- Model averaging
- Scoring rules
- Smoothing methods
- Spatial statistics
- Statistical inverse problems

## Data Science and Quantitative Genetics

### Agriculture and Industry

- Animal breeding
- Horticulture
- Data analytics

### Computational Methods

- Evolutionary biology and evolution
- Genomics
- Spatial analysis
- Chemometrics

### Health Sciences

- Applied genomics
- Medical genetics
- Māori-focussed health research

### Te Ao Māori

- Bioethics
- Culturally informed study (co)design
- Indigenous data sovereignty
- Disease risk estimation
- Mātauranga Māori in medical genomics and primary sector breeding

## Postgraduate research opportunities

Read about current PhD and Master's topics available at the University of Otago and find the research opportunity that's right for you.

Find out more about our academic staff and their research interests

Explore postgraduate research opportunities at Otago