Researcher

Professor Gary Froyland

My Expertise

Chaos theory, dynamical systems, complex systems, nonlinear dynamics, ocean circulation, fluid flow, optimisation, cancer radiotherapy optimisation, logistics, airline scheduling, rail scheduling, train scheduling, open pit mine planning, mathematics, dynamics, modelling, mathematical modelling, functional analysis, ergodic theory, differential geometry, Riemannian geometry.

Fields of Research (FoR)

Applied Mathematics, Pure Mathematics, Numerical and Computational Mathematics, Ordinary Differential Equations, Difference Equations and Dynamical Systems, Dynamical Systems in Applications, Optimisation, Operations Research

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Biography

Professor Gary Froyland works in two main research areas:  Dynamical Systems and Optimisation.  Dynamical Systems studies processes that change over time and optimisation concerns the mathematics of decision-making.  My research ranges from pure mathematics through to computation and application to industry and other scientific disciplines.

My dynamical systems research focusses on the interplay of probability and geometry in nonlinear and...view more

Professor Gary Froyland works in two main research areas:  Dynamical Systems and Optimisation.  Dynamical Systems studies processes that change over time and optimisation concerns the mathematics of decision-making.  My research ranges from pure mathematics through to computation and application to industry and other scientific disciplines.

My dynamical systems research focusses on the interplay of probability and geometry in nonlinear and chaotic dynamical systems, and uses techniques from ergodic theory, functional analysis, and differential geometry. In addition to fundamental mathematical research in dynamical systems, I have applied my research methods to analyse models of the ocean and atmosphere, and granular flow. My optimisation research is focused on decision making in large and complicated systems, sometimes in the presence of uncertain information. My research concerns new modelling approaches in mathematical programming, integer programming, and stochastic programming. These new approaches have been applied to strategic planning of open pit mines, scheduling of maritime crane fleets, and robust scheduling of aircraft and flight crews under uncertain disruption. Current work includes optimising lung cancer radiotherapy treatment.


My Grants

  • 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

  • Einstein Visiting Fellow, 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 (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)
  • Golda Meir – Einstein Institute of Mathematics Fellowship (1997, declined)

My Research Activities

Current Editorial and Other Duties 

  • Member of ARC College of Experts
  • 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

  • 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


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
  • Topics in integer programming and combinatorial optimisation
  • Stochastic integer programming

Currently supervising

Please refer to my personal webpage.

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Location

School of Mathematics and Statistics
University of New South Wales
Sydney NSW 2052
The Red Centre
Room 3060

Map reference (Google map)

Contact

9385 7050
9385 7123