Professor Gary Froyland

Professor Gary Froyland

Fields of research: Applied Mathematics, Pure Mathematics, Numerical and Computational Mathematics, Ordinary Differential Equations, Difference Equations and Dynamical Systems, Dynamical Systems in Applications, Optimisation, Operations Research
Campus: Kensington
Tags: Expanding Knowledge in the Mathematical Sciences, Expanding Knowledge in the Physical Sciences, Atmospheric Processes and Dynamics, Marine Oceanic Processes (excl. climate related), Primary Mining and Extraction of Mineral Resources, Air Passenger Transport, Air Freight, Rail Freight, Rail Infrastructure and Networks, Road Infrastructure and Networks, Road Public Transport, Antarctic and Sub-Antarctic Oceanography, Cancer and Related Disorders

ABOUT ME

My research spans two 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.

Education

  • BSc (Hons 1, Medal) Qld; (Pure and Applied Mathematics)
  • PhD W.Aust.; (Mathematics)

RESEARCH

 

Research in Detail

My dynamical systems research focusses...

ABOUT ME

My research spans two 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.

Education

  • BSc (Hons 1, Medal) Qld; (Pure and Applied Mathematics)
  • PhD W.Aust.; (Mathematics)

RESEARCH

 

Research in Detail

My dynamical systems research focusses on the interplay of probability and geometry in nonlinear and chaotic dynamical systems, and uses tools from ergodic theory. In addition to fundamental mathematical research in dynamical systems, I have applied my research methods to analyse models of the ocean and atmosphere, where I have mapped important physical features to significantly greater precision than existing methods.  These features include

  • Antarctic oceanic gyres
  • the Antarctic polar vortex, which traps chemicals in the stratosphere and is responsible for the ozone hole and weather patterns in Southern Australia.
  • Oceanic eddies (Agulhas rings) off the South African coast, which are responsible for the transport of heat and carbon from the Indian to Atlantic oceans.

My optimisation research is focussed on decision making in large and complicated systems, sometimes in the presence of uncertain information. My research is on new modelling approaches in mathematical programming, integer programming, and stochastic programming. I have applied my research methods to improve decision making to:

  • increase Net Present Value of open pit mining projects (BHP Billiton)
  • efficiently plan the movement of international shipping containers (Patrick Corporation)
  • timetable and schedule airline operations to mitigate the effects of unforseen delays 
  • optimise the delivery of high-powered radiotherapy to lung cancer patients (Cancer Australia, current work)

Research Grants

  • 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)

Current Student Projects (PhD and Honours)

Details can be found at my personal homepage.

  • Topics in dynamical systems and ergodic theory.
  • Transfer operator analysis with applications to fluid mixing
  • Lagrangian coherent structures in ocean and atmosphere models
  • Topics in integer programming and combinatorial optimisation
  • Stochastic integer programming
  • Polyhedral analysis of fundamental problems 

Supervision Opportunities/Areas

As above.

 

AWARDS & ACHIEVEMENTS

 

  • 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 (declined)
 

TEACHING & OUTREACH

 

 Courses I teach

  • Math3201 (Dynamical Systems and Chaos)
  • Math3041 (Mathematical Modelling for the Real World - Discrete Optimisation component)
  • Math5175 (Ergodic Theory, Dynamical Systems, and Applications)

Professional affiliations and service positions

  • Deputy Director of the Australian Mathematical Sciences Institute (AMSI).
  • Editorial Board for the Australian Mathematical Society's Lecture Note Series.
  • Editorial Board for Journal of Computational Dynamics.
  • Director of Honours Programs, School of Mathematics and Statistics, UNSW.

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 Expertise

Chaos theory, dynamical systems, complex systems, ocean circulation, fluid flow, optimisation, logistics, airline scheduling, rail scheduling, train scheduling, open pit mine planning, mathematics, dynamics, modelling, mathematical modelling.

Location

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


 

Map reference (Google Maps)

Contact

9385 7050
9385 7123