Mathematics, dynamical systems, complex systems, chaos theory, nonlinear dynamics, functional analysis, operator theory, ergodic theory, Riemannian geometry, fluid dynamics, geophysical fluid dynamics, ocean circulation, atmospheric dynamics, climate dynamics, machine learning, optimisation, open pit mine planning, logistics, airline scheduling, rail scheduling, train scheduling, cancer radiotherapy optimisation, mathematical modelling.
Scientia Professor Gary Froyland leads the ARC Laureate Centre for Dynamical Systems and Data. His main areas of interest are Dynamical Systems, Machine Learning, and Optimisation. His research ranges from pure mathematics through to computation and application to industry and other scientific disciplines.
His dynamical systems research lies at the interface of probability, geometry, operator theory, and learning in nonlinear and chaotic...view more
Scientia Professor Gary Froyland leads the ARC Laureate Centre for Dynamical Systems and Data. His main areas of interest are Dynamical Systems, Machine Learning, and Optimisation. His research ranges from pure mathematics through to computation and application to industry and other scientific disciplines.
His dynamical systems research lies at the interface of probability, geometry, operator theory, and learning in nonlinear and chaotic dynamical systems, and uses techniques from ergodic theory, functional analysis, Riemannian geometry, and machine learning. In addition to fundamental mathematical research in dynamical systems, he continues to apply his research methods to make discoveries concerning the dynamics of fluids, the ocean, the atmosphere, and the Earth's climate. His optimisation research addresses decision making in large and complicated systems, sometimes in the presence of uncertain information. His techniques have been applied to strategic planning of open pit mines, scheduling of maritime crane fleets, robust scheduling of aircraft and flight crews under uncertain disruption, and optimising lung cancer radiotherapy treatment.
My Grants
- ARC Laureate Fellowship (2024-2029) "Breakthrough mathematics for dynamical systems and data"
- Einstein Visiting Fellowship (2022-2026) "Coherent dynamics in complex systems with applications to engineering, geophysical, and social systems"
- ARC Discovery Project (2022-2024) "Which predictions can we trust? Stability of chaotic random dynamical systems" (with C. Gonzalez-Tokman and A. Quas)
- ARC Discovery Project (2021-2023) "Modern mathematics to unravel the birth of coherence in dynamical systems".
- Universities Australia - Germany Joint Research Co-operation Scheme (2020-2021): "How does turbulence work?" (with P. Koltai)
- ARC Discovery Project (2018-2020) "New mathematics for quantification and assessment of fluctuations and extremes in time-dependent dynamical systems" (with C. Gonzalez-Tokman, S. Vaienti, and E. van Sebille)
- NHMRC Project Grant (2018-2020) "Very fast, accurate and low dose imaging for radiotherapy treatments" (with R. O’Brien, J-J. Sonke, S. Vinod, and C-C. Shieh)
- Cancer Australia (2017-2019): "High Precision Radiotherapy: Dual Cardiac and Respiratory Motion Management" (with R. O'Brien, J. Booth, P. Bannon, and F. Hegi-Johnson)
- Universities Australia-Germany Joint Research Co-operation Scheme (2017-2018): "Robust detection and prediction of coherent structures in geophysical, physical, and chemical systems" (with O. Junge)
- Cancer Australia (2015-2017): "Reducing thoracic imaging dose and improving image quality in radiotherapy treatments" (with R. O'Brien and J-J. Sonke)
- ARC Discovery Project (2015-2017): "Discovery and tracking of coherent structures in geophysical flows" (with M. Dellnitz, O. Junge, and A. Quas)
- ARC Future Fellowship (2012-2015): "A probabilistic and geometric understanding of transport and metastability in mathematical geophysical flows"
- ARC Discovery Project (2012-2014): "Extracting macroscopic variables and their dynamics in multiscale systems with metastable states" (with G. Gottwald)
- ARC Discovery Project (2011-2013): "Innovative mathematics using transfer operators to reveal hidden ordered structures in geophysical flows" (with M. Dellnitz and A. Quas)
- Go8-Germany Joint Research Co-operation Scheme (2010-2011): "The climatic and environmental impacts of ocean circulation: tracking ocean eddies" (with M. Dellnitz)
- Chief Investigator (2008-2013), ARC Centre of Excellence for Mathematics and Statistics of Complex Systems.
- ARC Discovery Project (2007-2009): "A Dynamical Systems Approach to Mapping Southern Ocean Circulation Pathways" (with M. Dellnitz and A. Treguier)
- 2006 John Yu Fellowship to Europe
- ARC Linkage Project (2005-2007): "A Mathematical Approach to Flexible Management of Open Pit Mines with Uncertain Geology and Unpredictable Demand" (with N.Boland).
- ARC Linkage Project (2003-2004): "Using Mathematics to Maximise the Value of Open Pit Mines" (with N. Boland and P. Taylor)
Externally funded projects
- External Funding (Defence Science and Technology Organisation). “Scheduling of amphibious operations and efficient ship packing”.
- External Funding (NSW Department of Crime Research and Statistics). "Prison populations and correctional outlays: The effect of reducing re-imprisonment" (with Don Weatherburn)
- External Funding (Hunter Valley Coal Chain Logistics Team): "Increasing Throughput at Newcastle Port" (with P. Pudney)
- External Funding (Patrick Corporation): "Increasing Container Handling Efficiency at Port Botany" (with MASCOS -- UNSW & UniMelb, and Matheon)
- External Funding (BHP Billiton): "Mine Modelling, Optimization, and Valuation"
My Qualifications
BSc (Hons 1, Medal) Qld (Pure and Applied Mathematics); PhD W.Aust. (Mathematics)
My Awards
- Renewal of Einstein Visiting Fellowship, Einstein Foundation Berlin (2025-2026)
- Elected Member of the Academy of Europe / Academia Europaea (2024)
- ARC Laureate Fellow (2024-2029)
- Einstein Visiting Fellowship, Einstein Foundation Berlin (2022-2024)
- Fellow of the Society for Industrial and Applied Mathematics (SIAM) (2021)
- Fellow of the Australian Academy of Science (2020)
- Fellow of the Royal Society of New South Wales (2019)
- Fellow of Australian Mathematical Society (2017)
- John von Neumann Visiting Professorship, Technische Universität München (2016)
- Visiting Scholar, Initiative d’Excellence de l’université de Bordeaux (2016)
- Vice-Chancellor’s Award for Teaching Excellence - Postgraduate Research Supervision (2015)
- Erskine Visiting Fellowship, University of Canterbury (2013)
- ARC Future Fellowship (2012-2015)
- John Yu Fellowship (2006)
- BHP Billiton Innovation Prize (2004)
- Australian Academy of Sciences / Japan Society for the Promotion of Science Fellowship (1997-99)
My Research Activities
Recent Keynote Invitations
- International Congress on Industrial and Applied Mathematics (ICIAM) 2023
- SIAM Conference on Mathematics of Planet Earth 2020
- Equadiff 2019
- SIAM Conference on Applications of Dynamical Systems 2017
- SIAM Annual Meeting 2016
Current Editorial and Other Duties
- Editor-in-Chief of Australian Mathematical Society Lecture Series
- Editorial Board of SIAM Journal on Applied Dynamical Systems
- Editorial Board of Physica D.
- Editorial Board of Stochastics and Dynamics.
- Editorial Board of the Journal of Computational Dynamics.
Service positions
- National Committee for Mathematical Sciences, Australian Academy of Science (2022-).
- Member of ARC College of Experts (2021-2023)
- Head of Fundamental Data Science, UNSW Data Science Hub (2020-).
- Director of Postgraduate Research (Future Students), UNSW School of Mathematics and Statistics, (2019-2020).
- Scientific Committee of the MATRIX Research Centre, UniMelb, (2015-2019).
- Deputy Director of the Australian Mathematical Sciences Institute - AMSI, (2014-2016).
My Research Supervision
Supervision keywords
Areas of supervision
Details can be found at my personal webpage.
- Topics in dynamical systems and ergodic theory.
- Operator-theoretic approaches to machine learning
- Stability of linear operator cocycles
- Differential and spectral geometry with applications to fluid mixing and machine learning
- Lagrangian coherent structures in ocean and atmosphere models
- Lagrangian coherent structures in haemodynamics
- Optimising fluid mixing
- Nonlinear and mixed integer linear optimization with application to radiotherapy
Currently supervising
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https://orcid.org/0000-0002-2995-0582