Mathematics & Statistics
The School of Mathematics and Statistics is one of the largest mathematics schools in Australia and pursues a vigorous program of teaching, scholarship and research. It was formed in 1991 by merging the Departments of Pure Mathematics, Applied Mathematics and Mathematical Statistics. In particular, the postgraduate program is varied and flexible, catering for students of many different backgrounds. The School supports a policy of active research and insists on the highest standards of academic achievement. At present, the School consists of four research groups: Applied Mathematics, Mathematical Statistics, Nonlinear Analysis and Pure Mathematics. The School also hosts the Centre for Mathematical Biology, a University research centre. The School holds regular seminars, workshops and conferences which ensure that its members stay abreast of latest developments. It also supports an active program of long term and short term visits by distinguished international academics.
University of Sydney Advantage
The School of Mathematics and Statistics is one of the most successful mathematics schools in Australia at attracting research grants and it has a high profile internationally. The School provides a dynamic environment for postdoctoral fellows and a vibrant postgraduate community. In addition to its achievements in research, the School is notable for its development of MAGMA, a world class computational algebra and number theory package which is used in industry and by many branches of pure and applied mathematics.
Facilities
The School has all the facilities of a well-established and progressive teaching and research institution, including including access to a modern library and an extensive computer network of workstations. In addition the network supports a number of high-speed processors and colour graphics systems. A wide variety of software packages for computation in algebra, numerical analysis and statistics is available for use in both teaching and research, including Gap, Magma (developed within the School), Reduce, Mathematica and Matlab.
The School is proud of its postgraduate students. Our research students are a valuable resource and the School is committed to providing them with excellent research facilities and office space in which to work. Some financial aid is available to students to allow them to attend relevant conferences and workshops. Further support is offered in the form of part-time teaching, assignment and examination marking.
The School has an extensive computer network, running a mixture of Linux and Microsoft Windows, which is used for both teaching and research. All staff and postgraduate students are equipped with an office computer connected to the School network; there are computer laboratories for teaching. For numerical calculations the School maintains a dedicated cluster of fast dual processor Linux machines. SUN workstations and servers are used by the Magma group for research in computational algebra.
Areas of Research
The School is divided into four research groups: Pure Mathematics (with a strong subgroup structure consisting of algebra, analysis, geometry and topology); Applied Mathematics; Non-Linear Analysis; and Statistics.
Algebra
- algebraic geometry
- algebraic combinatorics
- finite groups
- Hecke algebras
- Lie groups and algebraic group
- representation theory of groups and algebras
- quantum groups and Yangians
- semigroups and formal language theory
Analysis
- harmonic analysis
- functional analysis
- random walks on groups
- groups acting on trees and buildings
Astrophysical and Geophysical Modelling
- numerical geophysical fluid dynamics
- pattern formation in the atmosphere
- solar physics
- nonlinear waves
- chaotic advection
- oceanography
- stellar and planetary dynamo theory
- magnetohydrodynamics
- geomagnetism
Computational algebra and number theory
- finitely presented groups
- permutation and matrix groups
- soluble groups
- Lie groups and representation theory
- factorisation of integers and primality testing
- local and global fields
- homological algebra
- polynomial factorization
- Groebner basis methods
- algebraic geometry and schemes
- finite geometry, designs, codes and graphs
- algebraic programming languages
- cryptography and coding theory
- signal processing and quantum computation
Financial Mathematics
- market microstructure models
- high-frequency equity price modelling
- real and exotic options
- stochastic volatility
- credit derivatives
- computational finance
- financial econometrics
Geometry and topology
- algebraic invariants of 4-manifolds
- knot theory
- homological group theory
- real and complex singularities
- stratifications and subanalytic sets
- Hodge theory
- topology of algebraic varieties
Industrial and biomedical modelling
- biomedical ultrasound
- medical engineering
- combustion
- metal coiling
- catalysis
- steel-rolling
- yarn production
- continuum mechanics
Mathematical biology
- collective behaviour and social insects
- biological pattern formation
- communication in neurons and neural systems
- synaptic function
- autonomic nervous system
- phylogenetics
Mathematical physics
- general relativity
- quantum field theory
- supersymmetry
- Lie algebras and Lie superalgebras
- quantum groups
Nonlinear analysis and applications
- computational neuroscience
- synaptic function, transmitter release and diffusion
- role of calcium in spontaneous and evoked release of neurotransmitter
- electrical conduction in nerves and muscle tissue
- dynamical systems
- completely integrable partial differential equations
- singularity analysis
- Painlevé equations
- boundary value problems
- nonlinear elliptic and parabolic equations
Nonlinear systems
- integrable systems
- solitons in nonlinear optics and fluid dynamics
- chaos
- asymptotic methods
- perturbation theory
Statistics
- probability theory
- limit theorems and approximations
- martingale theory
- exchangeability
- stochastic processes
- saddlepoint approximations
- limit results for U-statistics and M-estimators
- Levy processes
- bioinformatics
- motif finding
- biological modelling
- mixture models
- ruin theory
- computational statistics
- Markov chain Monte Carlo algorithms
- resampling analysis
- time series analysis
- generalised linear mixed models
- multivariate analysis
- change-point models
Academic Programs offered
- Honours
- Graduate Diploma in Science (GradDipSc)
- Master of Science (MSc)
- Doctor of Philosophy (PhD)