Advancing the mathematical and physical sciences

Our research attracts substantial external funding, and is regularly published in leading international journals.

We deliver outstanding outcomes and create impact for end-users, and collaborate widely at both national and international levels. Our research is also supported by a vibrant seminar series, attracting both domestic and international speakers as well as talks by members of the School.

Areas of research excellence

We’re nationally and internationally recognised for our areas of research excellence:

Our analysis research spans harmonic analysis, functional analysis, geometric analysis and partial differential equations. Some of the problems we've studied include mathematical formulations of physical situations, and the solutions we've produced have real-world applications.

Our research interests in analysis include fundamental and prominent problems in harmonic analysis and their applications to functional analysis, partial differential equations and several complex variables. Some of our research topics are estimates on various singular integrals on different types of function spaces, characterisations of commutators on function spaces, studies of important operators such as the Schrödinger operators and non-linear partial differential equations and systems in different settings.

Our research interests in geometric analysis include the advanced study of curvature flows and its applications in physics and geometry.

Contact us

To learn more about our analysis research, contact professor Xuan Duong.

Astronomy and astrophysics are the study our universe. Astrophotonics is the manipulation and processing of light to improve our view of the universe.

Research Centre for Astronomy, Astrophysics and Astrophotonics

Our research centre answers the big questions about our cosmos by conducting research on topics ranging from alien planets to distant galaxies, using optical and radio telescopes as well as computer simulations.

Visit our research centre website.

Contact us

To learn more about our astronomy, astrophysics and astrophotonics research, visit our website or contact Professor Orsola De Marco.

Category theory is a branch of mathematics which seeks to identify patterns and structures across diverse areas of mathematical discourse, and to distil them down to their essential nature. In this way, it allows these areas to enhance each other, leading to broader application.

Centre of Australian Category Theory (CoACT)

CoACT members are pioneers of monoidal, enriched, and higher-dimensional category theory – areas which are increasingly fundamental to modern algebraic geometry, representation theory and mathematical physics.

Other fields CoACT’s research has influenced include algebraic topology and homotopy theory, programming language semantics and quantum groups.

At the heart of CoACT’s activities is the Australian Category Seminar which meets weekly and is frequently visited by major international figures in category theory and cognate disciplines.

Contact us

To learn more about our category theory research, contact Associate Professor Richard Garner.

Photonics is the science and technology of light. Our research aims to address key challenges in advanced manufacturing, environmental sensing, astronomy, medical technologies, energy, defence and security.

MQ Photonics

MQ Photonics Research Centre is led by Centre Director, Professor Judith Dawes. We are a group of scientists and engineers who do amazing things with light.

Contact us

To learn more about our photonics research, visit our website or contact Professor Judith Dawes.

ARC Centre of Excellence for Engineered Quantum Systems (EQuS)

We are a part of an Australian Research Council (ARC) Centre of Excellence, through which much of our research is channelled.

EQuS has a vision "to conduct world-leading research to exploit the potential of quantum science and develop a range of transformational technologies that will benefit society."

Associate Professor Thomas Volz is the Chief Investigator and Node Manager of the research team at the Macquarie node of EQuS. Other members include Professor Gavin Brennen, Associate Professor Daniel Burgarth and Dr Cyril Laplane.

Visit the EQuS website.

Sydney Quantum Academy (SQA)

We are part of the Sydney Quantum Academy. Its vision is to build Australia’s quantum economy. Collaborating with academia, industry and government, SQA will harness Sydney’s collective quantum expertise to develop diverse talent and a globally recognised quantum ecosystem.

Visit the SQA website.

The Macquarie Centre for Quantum Engineering (MQCQE)

MQCQE incorporates the Macquarie EQuS research team. Led by Centre Director Professor Gavin Brennen, MQCQE explores the complex world of the quantum to probe the quantum nature of reality.

Learn more at the MQCQE website.

ARC Centre of Excellence for Nanoscale Biophotonics (CNBP)

CNBP aimed to "drive the development of new devices to measure and sense at the nanoscale level, providing powerful new ways of understanding cellular processes within the human body."

Node Leader and Chief Investigator Professor Jim Piper (AM) lead the Advanced Detection & Imaging research team at the Macquarie node of CNBP.

Visit the CNBP website.

Contact us

To learn more about our quantum information science research, contact Professor Gavin Brennen.

Members of the statistical modelling for complex data group exploit modern statistical and computational cutting-edge methods to tackle a variety of real-world problems from small, designed studies to large-scale high-dimensional data challenges. Our research involves tight coupling between applied statistics and statistical theory to offer novel statistics methodology and computational technology for evidence based science discovery.

Some of our research strengths include Bayesian modelling, dimension reduction, variable selection, survival analysis, nonparametric statistics, statistical software development, optimal decision making, bootstrap techniques, Monte Carlo methods, change-point detection and machine learning algorithms. Applications of our statistical methodology include bioinformatics, genomics, neuroimaging, biology, ecological studies, insurance, finance, economics, medicine, defence, and quantum computing.

Our group has well-established research collaborations with industry and other universities such as the Australian National University,  Imperial College London, University of California, University of Copenhagen, The University of Queensland and The University of Sydney.

Contact us

To learn more about our statistical modelling for complex data research, contact Professor Benoit Liquet.

The members of the waves, dynamics and modelling group use mathematical and computational methods to explore physical phenomena arising from the natural world. We study a range of problems from fluid dynamics, ecology and biology, electromagnetism and other physical systems. We create new mathematical and computational techniques to explain what happens in these systems and predict what they might do in the future.

Our research strengths include nonlinear waves, boundary layers in fluids, pattern formation, wave scattering and diffraction, collective behaviour, and asymptotic techniques.

Contact us

To learn more about our waves, dynamics and modelling research, contact Chris Lustri.

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Last updated: 07 Jul 2022