Mathematical Sciences research

Research areas

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• Analysis, Differential Equations, and Computation

  Group leader Prof. Murray Elder

  Focus

  • Analysis
  • Differential equations
  • Complex systems
  • Climate modelling
  • Computing
  • Formal languages
  • Geometric group theory

  Research in the Analysis, Differential Equations and Computation group spans a range of activities that focus on the abstract structure of mathematics. A strong research focus is in Modern Analysis, including Harmonic Analysis and dynamical systems, as well as Lie symmetries and the solution of differential equations. The group also maintains expertise in computational weather modelling and climate forecasting. An additional and growing research area is in the theory that underlies efficient computing; this includes abstract algebra, Group Theory, automata and formal languages, which all lie at the heart of what computers can (and can't) do. These areas have applications ranging from climate prediction, data mining, information theory and theoretical Quantum Mechanics.

• Financial Mathematics and Stochastic analysis

  Group leader Prof. Erik Schlogl

  Focus

  • Quantitative Finance
  • Stochastic Processes
  • Financial Mathematics
  • Risk Management
  • Financial Markets

  Stochastic analysis is the mathematical theory that allows one to model dynamic random phenomena. Such phenomena arise almost everywhere in the real world.

  Particularly important instances are the behavior of financial markets and the study of risk in a wider sense. To be able to obtain quantitative results one needs stochastic numerical methods and also sophisticated statistical techniques. Additionally, many tasks involve some stochastic optimisation, or the solution of partial differential equations. The group focuses on developing the theoretical and practical tools needed to allow us to model and quantitatively handle challenging applied problems across a broad range of fields, with a special focus on quantitative methods in finance, statistics and physics.

• Mathematics and Science Education

  Group leader A/Prof. Mary Coupland

  Focus

  • Transition from school to university
  • Motivation
  • Metacognition
  • Academic achievement
  • Quantitative literacy
  • Engagement
  • STEM in schools

  Members of this group conduct research in undergraduate mathematics and science teaching and learning, with some cross over into schools. Funding has been received from the Federal government for the Maths Inside project, and from internal sources such as the First Year Experience project of UTS. We aim to understand and to promote the learning of our students by researching motivation and engagement. We also investigate learning in the new large collaborative learning spaces at UTS. We maintain links with the School of Education in the Faculty of Arts and Social Sciences.

• Optimisation and Operations Research

  Research leader A/Prof. Yakov Zinder

  Focus

  • Optimisation
  • Industrial optimisation
  • Logistics
  • Linear Programming

  Optimisation is one of the most rapidly evolving fields of modern mathematics. The members of the Group are actively involved in the development of new optimisation techniques and their practical applications. Our research focuses primarily on combinatorial optimisation and large scale mixed integer linear programming. The results of our research are published in first-tier international journals and refereed proceedings of prestigious international conferences. Active industry collaboration is central to the group: The practical applications encompass planning and scheduling problems arising in different fields from manufacturing and transportation to professional training.

• Statistics and Data Science

  Group leaders

  Professor James Brown
  Professor Sally Cripps
  Professor Matt Wand

  Focus

  • Bayesian computing
  • Scalable methodology
  • Data science
  • Health statistics
  • Population statistics
  • Statistical modelling

  The UTS Statistics and Data Science group has interests that range from the development of fundamental statistical methods to the application of statistics in such areas as population health, forensics, and law. Much of this work is funded through grants from the Australian Research Council, as well as as well as through Australia's National Health and Medical Research Council (NHMRC) project grants, the Bill and Melinda Gates Foundation, and cooperation with Australian government bodies such as the Australian Bureau of Statistics. A major part of our work involves the development of new methodology to investigate complex problems in the age of Big Data. Specific sub-areas of statistical research include:

  • Methodology for Big Data - development of scalable statistical methodology for analysis of high volume/velocity data involving machine learning paradigms;
  • Health related statistics - applications of statistical modelling within population health, sports science, and clinical trials;
    Statistical data science  - applications of machine learning to generate quantitative information for legal scholars, data wrangling and analysis of medical data;
  • Official statistics - use of government surveys combined with census and alternative data sources to produce key population statistics;
  • Modelling and simulation of stochastic processes - development of methodology for the modelling and simulation of natural phenomena including applications in biology.

• Theoretical Photonics

  Group leader Prof. Christopher Poulton

  Focus

  • Photonics
  • Electromagnetism
  • WaveTheory
  • Metasurfaces
  • Complex systems

  Photonics is the science of how light behaves in complex systems and on the nanoscale. The UTS theoretical photonics group focuses on the solution of difficult theoretical problems in modern nanophotonics, as well as in the creation of new, highly-accurate models that are used in cutting-edge photonics experiments. Our particular areas of research focus are in metamaterials and metasurfaces  - highly complex structures with optical properties beyond those occurring in nature, and nonlinear phononics - in which light and sound interact on the nanoscale. This research area overlaps with the photonics group within the Physics Discipline.